Jorge Pullin: Okay, so our speaker today is that Wilson was going to speak about black hole collapse and bounced and effective move quantum gravity.
Jorge Pullin: It.
Edward Wilson-Ewing (UNB): Right. Thank you very much. Um, so what I'll tell you today is some work that I've been doing with two students that you envy Jared Kelly and Robert Santa Cruz and you can find
Edward Wilson-Ewing (UNB): The papers.
Edward Wilson-Ewing (UNB): That my talks based on on the archive at these two numbers.
Edward Wilson-Ewing (UNB): Okay, so my goal today is to explain the basic ideas and results. So especially what goes in to the calculation and what comes out. I won't spend so much time on the details of the intermediate calculations and I'll just refer you to the papers for those details.
Edward Wilson-Ewing (UNB): Okay.
Edward Wilson-Ewing (UNB): So, as I think everyone here knows black holes were in the most promising places to explore and potentially even test any theory of quantum gravity and there are three topics that are
Edward Wilson-Ewing (UNB): Three reasons for that, that stand out among several others. So first of course in classical general relativity black hole contains a curvature singularity.
Edward Wilson-Ewing (UNB): And we'd expect the quantum gravity affects would become important in the vicinity and possibly resolve that singularity.
Edward Wilson-Ewing (UNB): Second, there's the famous information last problem. So if you use quantum field theory on a curve background. If you create a black hole.
Edward Wilson-Ewing (UNB): By collapsing some matter that's in a pure state, then the black hole will act as a black body and it appears to evaporate to mix state of Hawking radiation.
Edward Wilson-Ewing (UNB): So the question is, Can quantum gravity somehow restore unitary in this process. And finally, there have been some recent suggestions that perhaps quantum gravity affects could cause a black hole to transition to a white hole. So, this
Edward Wilson-Ewing (UNB): Is built in, in part on results in the porn cosmology, where we see that we have a cosmic bounce. And so the idea is perhaps something similar could happen inside a black hole where you'd have a star that collapses. Once a black hole and then bounces and comes back out.
Edward Wilson-Ewing (UNB): So our goal in this work is to use elocution LTC techniques to study quantum route effects and black holes in general and to hopefully have something to say about these different problems.
Edward Wilson-Ewing (UNB): Okay. So the general framework that all follow in this talk is that we're going to look at spherical symmetric last whole space times
Edward Wilson-Ewing (UNB): So this is really short. So we're not looking at career. There's no angular momentum here.
Edward Wilson-Ewing (UNB): And and how we're going to do this is we're going to start by imposing spherical symmetry. The classical both in the constraints and the syntactic structure.
Edward Wilson-Ewing (UNB): Then we're going to further simplify the problem by gauge fixing the different more physical constraint began at the classical level. So these first two steps, make no reference at all to quantum gravity.
Edward Wilson-Ewing (UNB): Then the third step is that will include salami corrections in an effective framework and this is going to build on the work by a lot of people, the list here is by no means exhaustive.
Edward Wilson-Ewing (UNB): Have only listed the papers that we follow the most closely the literature here is huge. And there are a lot of other important papers here which I just don't have a place to write down. Then once we have
Edward Wilson-Ewing (UNB): Our
Edward Wilson-Ewing (UNB): Hamiltonian constraint, then we can find and solve the effect of equations emotion and see what we get. So that's the general process that will follow here.
Edward Wilson-Ewing (UNB): What we do is that we start with vacuum space time. So the first half of my talk will really be focusing on a vacuum space time
Edward Wilson-Ewing (UNB): But a quite interesting result is that the space time that we get when we focus on a vacuum of space time is incomplete.
Edward Wilson-Ewing (UNB): And this will be a little bit clearer as we go on. But really, what happens is that we have a hole in the middle. Something's missing.
Edward Wilson-Ewing (UNB): And what we were what we did is that we added a dust field and this lets us do two things. First, let's a steady the collapse. So we're no longer just looking at stationary solution to the effective equations emotion, but we can look at the collapse of some matter.
Edward Wilson-Ewing (UNB): And on top of that, with this were able to describe the entire platform space time including that whole that shows up when you only look at the vacuum case. So in this framework, it seems that it's essential to include matter if you want to be able to describe the full space time
Edward Wilson-Ewing (UNB): Okay. So let me start here with just some basic information about the variables that will use. So if we work with a strictly symmetric metric, we can always put it in this form.
Edward Wilson-Ewing (UNB): We have some laps function. Here we have some shift vector here that only isn't the radial direction and then we have some functions in front of the radio part and some function for the angular part
Edward Wilson-Ewing (UNB): And as I mentioned, we impose the aerial gauge which means that we're taking this part, considering it equal to x squared.
Edward Wilson-Ewing (UNB): So this cage fixes the different more physical constraint. We're only left the scale or constraint and it also imposes the relationship between the shift and the laps.
Edward Wilson-Ewing (UNB): Okay, now here of course have introduced this little piece. So what is be be captures the extremes of curvature in the angular directions. So this is essentially
Edward Wilson-Ewing (UNB): A component of the extrovert connection in the angular directions. And in this case, it only captures the extremes of curvature its conjugate variable is the insights triad.
Edward Wilson-Ewing (UNB): Which
Edward Wilson-Ewing (UNB): In this case turns out to be the square root of f and g. So, this is the densities triad.
Edward Wilson-Ewing (UNB): That is conjugate to this component of the connection. Okay, now we're in vacuum spherical symmetry to start. So after we fix the aerial gauge. We only have to face space variables that remain.
Edward Wilson-Ewing (UNB): Be an EV, and of course
Edward Wilson-Ewing (UNB): We have circle cemetery, but we still have a degree of freedom in the real direction. So both of these qualities depend on x.
Edward Wilson-Ewing (UNB): As I already mentioned also we have one scanner constraint which is left and of course the exact form isn't so important. The main point is that it only depends on be an EB and then pecs and the rubber meets the premier
Edward Wilson-Ewing (UNB): Okay. And then finally, if we want to study the dynamics of the system, we can extract the equations emotion from the Hamiltonian constraint which is just integrating the scale or constraint over the radio.
Edward Wilson-Ewing (UNB): Coordinate with weighted by some laps function.
Edward Wilson-Ewing (UNB): Okay, so this is he basic classical framework that we want to take and pad. Hold on me corrections to
Edward Wilson-Ewing (UNB): So the key step here is that we want to express be this component of the astral Roberto connection in terms of its parallel transport among edges of a minimal length which is proportional to Planck length. So here delta is the area gap. And so we're going to take a
Edward Wilson-Ewing (UNB): Look, and consider the parallel transport along edges with a minimal length given by the square root of the area.
Edward Wilson-Ewing (UNB): So this has to be done, both in scale or constraint and also for the relation between and
Edward Wilson-Ewing (UNB): And the shift vector. So if I just go back one slide. If you remember, here we had this relationship between the shift in the radial direction and the laps and we have a be here. So that means that if I want to gamble to
Edward Wilson-Ewing (UNB): Promote this expression to an operator and a quantum theory, I have to somehow replace this component to be also. So, of course, we're very familiar from the quantum cosmology of doing this in the scale or constraint here. But in this case, we also have to do it in this relation here.
Edward Wilson-Ewing (UNB): Okay, so this is
Edward Wilson-Ewing (UNB): The process have to fall to introduce our Columbia corrections. How do we do this well we create our, our edges and we just take the parallel transport along those edges. Now, a key point here, and this is something that was pointed out some time ago.
Edward Wilson-Ewing (UNB): When the introduction of the improved dynamics is that when we talk of the length of an edge, of course.
Edward Wilson-Ewing (UNB): We're referring to a physical length. We're not referring to a quarter length. So if we ask that the link
Edward Wilson-Ewing (UNB): That the only to the edge be let's say Planck length, then we're really referring to the physical length of that edge being the planck length and not some coordinate length being equal to the planck length.
Edward Wilson-Ewing (UNB): So here I have considering the tonal transport of my
Edward Wilson-Ewing (UNB): Of be in the angular directions. So, for example, like it just take it in the theta direction.
Edward Wilson-Ewing (UNB): And my metric tells me that the physical length is related to the court length theta in this way.
Edward Wilson-Ewing (UNB): So if I require that my physical length be of the order of the square root of delta. That means that my court length is related to the square root of delta in this way. So this is really just using the new bar dynamics from cosmology and extending it to
Edward Wilson-Ewing (UNB): To the black hole space time. And so if I do this, and I get this substitution for be that looks like this.
Edward Wilson-Ewing (UNB): And here I want to take this substitution and put it back in to the scale or constraint and replace the whatever be shows up I replace it by this quantity here.
Edward Wilson-Ewing (UNB): Okay, I just want to mention two quick technical points. These aren't so important going forward. But just for those of you who know this very well I'm, what I'm doing here is I'm really following what's known and lukewarm cosmology, as the Caleb quantization.
Edward Wilson-Ewing (UNB): And another important point is here, I really am calculating the password exponential when I'm evaluating the parallel transport.
Edward Wilson-Ewing (UNB): What happens is that because of spiritual symmetry as I integrate along an angular direction this path ordering just trivializes so it's very easy to handle
Edward Wilson-Ewing (UNB): If I were to take the peril transferring the radio direction course then because my connection would depend on the radio coordinate this path where he would not trivialize
Edward Wilson-Ewing (UNB): So this would be much more complicated, but this is one of the reasons why we did the gauge fixing earlier.
Edward Wilson-Ewing (UNB): Through the gauge fixing we now only have the components of the connection left that aren't angular direction. And in this case we can really calculate the full payroll transport explicitly and very easily.
Edward Wilson-Ewing (UNB): If we were to do it in the radio direction. This will be much more complicated. So that's one nice effect of doing this gauge fixing is that simplifies the problem significantly for us.
Parampreet Singh: It. Can I ask you a question.
Edward Wilson-Ewing (UNB): Yes, please.
Parampreet Singh: So if I understand now your strategy correctly. So first we are doing the aerial gauge fixing so we are not worried about the radial coordinate and how do we call them is over there. But in addition
Parampreet Singh: We are only considering the wholeness of extrinsic curvature on even on this aerial gauge so
Parampreet Singh: That's right. If one doesn't do that.
Parampreet Singh: Then this. I'm not sure. Like how you got this formula like are you driving it explicitly from the Hamiltonian constraint standing on the quantum Hamiltonian constraint.
Parampreet Singh: Or you're using it as a tumble, like many people, many people use because I was worried about what happened to the spatial curvature part
Parampreet Singh: Raven to the k quantization because we know that if we do the
Parampreet Singh: Loop Quantum cosmology are gonna close model than this tumble doesn't apply.
Edward Wilson-Ewing (UNB): Right. So, here what we're doing.
Edward Wilson-Ewing (UNB): Is we're
Edward Wilson-Ewing (UNB): Calculating the the parallel transport, as you say, of the extremes of curvature in the angular direction. And here we're really are calculating the password exponential. And all of that is just that just so happens that trivializes do just vertical symmetry.
Edward Wilson-Ewing (UNB): Now you're right that there is some spatial curvature here and what would happen. It's exactly the same thing as a loop quantum cosmology. If we included the spatial curvature
Edward Wilson-Ewing (UNB): Then we would get something which is not almost periodic in the connection. And so then I wouldn't know how to represent it in the quantum theory.
Edward Wilson-Ewing (UNB): But we still the scanner constraint still knows about the spatial curvature, of course.
Parampreet Singh: So the scanner constraint knows about the spatial curvature only because of those extra terms which you didn't hold on a minute. Right.
Edward Wilson-Ewing (UNB): That's right.
Parampreet Singh: Well, the spatial coverage. So, too. So to put it the way you said it to put it correctly, the spatial curvature piece in your Hamiltonian constraint is not does not know about quantum geometry affects
Edward Wilson-Ewing (UNB): X plus. Correct. Yeah, okay.
Edward Wilson-Ewing (UNB): So of course, ideally, we'd like to include those also but then I'm not sure how to eventually construct a quantum theory with that.
Parampreet Singh: But just one last point, like I know it's technical for everyone. But didn't you tried like the way like it was done.
Parampreet Singh: Like in a PSP paper or what Cory cheon crummy did later with like this.
Parampreet Singh: Using the shaker connection itself as an operator.
Edward Wilson-Ewing (UNB): Um, yeah, so you can also do something like that, um, this just turns out to be easier.
Edward Wilson-Ewing (UNB): But also I mean if you remember in the paper that we wrote on this, we found that
Edward Wilson-Ewing (UNB): In in lukewarm cosmology, at least. I mean, I don't know if this is true for black holes, but certainly in cosmology. It seems that the Caleb quantization is closer to the F quantization than the quantization is
Parampreet Singh: Yes, I know that. Yeah.
Edward Wilson-Ewing (UNB): Yeah. So in that sense, I would prefer to work with the K quantization and the eight quantization here.
Edward Wilson-Ewing (UNB): In any case, the F quantization. I'm not sure how to do that because you'll definitely get something which is not almost periodic in the connection.
Parampreet Singh: Okay, thank you.
Parampreet Singh: No problem.
Edward Wilson-Ewing (UNB): Are there any other questions.
Edward Wilson-Ewing (UNB): Okay, so
Edward Wilson-Ewing (UNB): Here the the main point is that we're able to really express be in terms of the parallel transport and we're using the improved or new board dynamics to do this. Okay, now I want to say a few words about this because there's been a lot of work.
Edward Wilson-Ewing (UNB): On this topic in the context of black holes and we're going at it from a slightly different
Edward Wilson-Ewing (UNB): Perspective than what a lot of other people have done. And so I want to compare and contrast, a little bit.
Edward Wilson-Ewing (UNB): So this very same URL scheme was first proposed by Boomer van der Sloot quite some time ago and they applied in the contest key sex FaceTime, and that of course describes the black hole interior in GR
Edward Wilson-Ewing (UNB): But it turns out that if you use this choice and control ski Sachs, you get unacceptably large effects of the horizon, so of course for large black hole that
Edward Wilson-Ewing (UNB): Space Time permission, the pricing is very small and you would expect the classical JIRA would be a good approximation there.
Edward Wilson-Ewing (UNB): And what they found is that, on the other hand, that's not at all what happened. They got very large corrections at the horizon, even if the temperature was small and so
Edward Wilson-Ewing (UNB): We think, and that this problem is probably due to the fact that they were using courts that are coming on the horizon. Now what the improve dynamics scheme is really doing is that it's asking you to identify a physical length.
Edward Wilson-Ewing (UNB): Of an edge with the planck length, but if you take the full autonomy in a direction that becomes know that physical length, necessarily becomes zero. And if you're trying to force this zero to be equal to the planck length, it's not so surprising that you could run into some inconsistency.
Edward Wilson-Ewing (UNB): So,
Edward Wilson-Ewing (UNB): Our perspective on this is that the issue that
Edward Wilson-Ewing (UNB): arose in Boomer vendor suits work was not so much of their choice from you bar was incorrect, it was rather that they were trying to use it for corns that became know
Edward Wilson-Ewing (UNB): And when you have these coins that become know you're essentially forcing this physical length, which tends to zero to be equal to the planck length and you have some tension there.
Edward Wilson-Ewing (UNB): So,
Parampreet Singh: It can I make one comment.
Parampreet Singh: Yes. Is this is I don't think like there is anything. I'm sorry to say, but I don't see any new insight here like this was, this is already known in literature.
Parampreet Singh: If you look at my paper with Aunt and Joe like a few years back we had pointed out, essentially, that the bomb of understood approach fails.
Parampreet Singh: Precisely because one is trying to apply Mubarak scheme at the coordinate singularity and in my paper right away and how we are also we have commented on the same thing. So you're completely right that literature already supports your point.
Edward Wilson-Ewing (UNB): I'm happy with that.
Edward Wilson-Ewing (UNB): Okay. And so this is why. Now I'm trying to keep the same new bar scheme but now work with coordinates that cover the whole FaceTime
Edward Wilson-Ewing (UNB): Right. So instead of trying to adapt and move our scheme. I'm going to instead say okay, you know, let's keep that same URL scheme. But now let's use courts that don't become know anywhere.
Edward Wilson-Ewing (UNB): So this is, if you like. It's perhaps not a new insight, but this is the motivation behind what we're doing here.
Edward Wilson-Ewing (UNB): Okay, and
Edward Wilson-Ewing (UNB): So let's continue on this theme this issue of having these no coordinates we can avoid that by using horizon Pearson coordinates.
Edward Wilson-Ewing (UNB): And there's been some literature on this also. So chimney and Tang did some murkiness in 2012 and then very recently can be Neil meadow and pulling also worked on this. And of course, our work is also going this exact same direction.
Edward Wilson-Ewing (UNB): One issue though with the first work but union Tang was that they didn't have a closed algebra. So if you look at the constraint algebra between they're effective Skyler. And if your constraints that algebra didn't close so that obviously was a problem.
Edward Wilson-Ewing (UNB): And I think that this is due to the fact that they were using a point along the approximation, the radial direction.
Edward Wilson-Ewing (UNB): And of course, this is an in some ways a reasonable approximation to try because this means you don't have to evaluate this path or exponential, which becomes very messy very quickly.
Edward Wilson-Ewing (UNB): But it seems to me that this approximation. Although tempting just doesn't work. In this case, so
Edward Wilson-Ewing (UNB): From my point of view, I think that if you take this new our scheme and you apply it to the full space time. And so here I mean both the interior and the exterior of the black hole.
Edward Wilson-Ewing (UNB): We don't just restrict to contest the sax, then I think there are three ways that we could
Edward Wilson-Ewing (UNB): Hope to get a close constraint algebra. So the first one is just to avoid using the point. Hello enemies approximation.
Edward Wilson-Ewing (UNB): And instead, evaluate the password or exponential X for the connection components in the radial direction. Now this to me, I think, is ideal, but it also seems very hard. So to start, I didn't want to go down that route.
Edward Wilson-Ewing (UNB): Another way that you could approach this problem is to try different combinations of constraints. So again, being in Poland. Some time ago showed how you could
Edward Wilson-Ewing (UNB): redefine the constraints and get them the billion set of constraints and this lends itself to a very nice treatment, which was done recently by can't be any old metal and poor but and
Edward Wilson-Ewing (UNB): Please forgive me, correct me if I'm wrong, but as far as I understand, this works very well and vacuum. But I think it's harder to include matter in this case.
Edward Wilson-Ewing (UNB): Now our approach is different. We're going to oppose the gauge. So the different Mormonism, the aerial gauge to fix it. If you're more for some constraints in our case.
Edward Wilson-Ewing (UNB): And the advantage of this is that in this case it will be easy to add in a matter of field.
Edward Wilson-Ewing (UNB): Okay.
Edward Wilson-Ewing (UNB): Um, let me
Edward Wilson-Ewing (UNB): Go back to where we were. So we had found the Islamic corrections and we wanted to add them back into the scale of constraint. And so this gives us
Edward Wilson-Ewing (UNB): The effect of scale or constraint, they show you here.
Edward Wilson-Ewing (UNB): The details don't matter.
Edward Wilson-Ewing (UNB): The point is that from this of course we can derive the equations emotion that were interested in and then solve them.
Edward Wilson-Ewing (UNB): Okay. Now, of course, we fix the different Sufism fix the arrow gauge. So that gets rid of a few more physical constraints, but we still have an entry looking straight algebra between the scale or constraint in itself.
Edward Wilson-Ewing (UNB): And what's nice is that with this modification. So with these salami corrections here. We still have a constraint algebra that closes, of course, the, the algebra is different. We have this extra term here compared to what happens classically
Edward Wilson-Ewing (UNB): But we have a consistent theory with an algebra. The closest so that's that's an important point here.
Edward Wilson-Ewing (UNB): Now remember that we also had to update the relationship between the laps and the shift.
Edward Wilson-Ewing (UNB): So,
Abhay Vasant Ashtekar: But in the
Abhay Vasant Ashtekar: classical limit you probably get exactly
Abhay Vasant Ashtekar: What you should get right in this
Edward Wilson-Ewing (UNB): Absolutely. So the classical limit you take
Edward Wilson-Ewing (UNB): The square root of delta two zero. So this cosine goes to one. And then here, this square root of delta over x cancels this x over square root of delta and you get back the classical result absolutely right.
Like
Edward Wilson-Ewing (UNB): I'm okay so
Edward Wilson-Ewing (UNB): And this form of the constraint Alger was actually quite suggestive.
Edward Wilson-Ewing (UNB): Because the classical form, which I've given right here you can rewrite in terms of the shift vector by using the classical relationship between the shift in the laps. And so what we did is that we updated the relationship between the shift in the laps in this way.
Edward Wilson-Ewing (UNB): So that if we then use this relationship to re express this
Edward Wilson-Ewing (UNB): This term here in terms of
Edward Wilson-Ewing (UNB): This shift and the shift vector like this, using this relation then we get something that looks exactly like the classical case. So, here there is some ambiguity in the exact choice that you make. And we're, we're, guided by this resemblance to make this choice.
Okay.
Edward Wilson-Ewing (UNB): So now.
Parampreet Singh: Can I ask a question. So
Parampreet Singh: Yes, please. Like you already had a very natural choice between x and n right when you did polymerization of be so essentially you are
Parampreet Singh: Multiplying by one and then calling that one as cosine
Edward Wilson-Ewing (UNB): Um, well, in some sense, I would few this
Edward Wilson-Ewing (UNB): I think that it's a will be shouldn't assume that we have the same substitution everywhere.
Edward Wilson-Ewing (UNB): Right. I mean, in one case, something is coming from the field strength. And in the other case, there is a relationship between your look for your garage multipliers. So it's not obvious to me that you should necessarily do the same substitution everywhere.
Edward Wilson-Ewing (UNB): Okay, another night.
Edward Wilson-Ewing (UNB): Sorry, let me just mention quickly. This is exactly the same relation that can be Neil meadow and Poland gut and they chose it for a different reason. Which I thought was, was quite interesting and their point is that in the scale or constraint, you have this sign squared term here.
Edward Wilson-Ewing (UNB): And so what that means is that when you act with it, you will act, you will shift by twice to to to spatial steps.
Edward Wilson-Ewing (UNB): And here, if you only have a sign you only move by one. And so then your, your lattices in the quantum three won't quite match up.
Edward Wilson-Ewing (UNB): But if you include this cosine term here, then again, you'll shift by two steps in the spatial direction. So there's like a consistency there to sorry you're gonna say something else.
Parampreet Singh: Yes, and maybe then I'm just confused. So, earlier you also the relationship of Annex and and right and I thought you said that replace be by
Parampreet Singh: Expert scooter of telltale sign of delta V by x. So I assume that you are doing that at that step itself, but you are not doing that, you're not
Edward Wilson-Ewing (UNB): No, no.
Parampreet Singh: Okay.
Edward Wilson-Ewing (UNB): No, I'm doing that for the effect of scale or constraint here and then I still have to do it for that relationship between X Men.
Edward Wilson-Ewing (UNB): And that's what I'm doing at this step here.
Carlo Rovelli: Do you mind that is super simple technical thing that just to
Further
Carlo Rovelli: X X X X squared. This is the area of this of the of the proportion to the area of the of the sphere suicide. Correct. Yeah, so the question is, it connects to be negative.
No.
Edward Wilson-Ewing (UNB): I don't see how that would come out.
Edward Wilson-Ewing (UNB): This the data follow
Carlo Rovelli: The topology here is necessarily that if you follow if you continuously follow shrinking here. You cannot continue more than that. You don't have another side so
Edward Wilson-Ewing (UNB): Yeah, I
Edward Wilson-Ewing (UNB): I don't think that's actually an input, but then when I solve the equations emotion that's just what comes out, I guess.
Edward Wilson-Ewing (UNB): If something else came out, I would have been a bit surprised, to be honest. But I don't think that's a requirement at this stage.
Edward Wilson-Ewing (UNB): So I think, in principle, you could have negative access but that would. I'm not sure how I would interpret that. And it doesn't seem to be relevant for the solutions that we find
Parampreet Singh: Okay, can I ask one final question.
Edward Wilson-Ewing (UNB): Yes, please.
Parampreet Singh: I don't know like what was done in Germany Olmedo Poland paper, but are you saying that in both the papers, the strategy which one follows, is that okay like one polarizes be and
Parampreet Singh: One rights being in terms of the only the sign function in the Hamiltonian constraint. But, but when one has to relate, an expert and one has to use a very different polymerization
Edward Wilson-Ewing (UNB): I wouldn't call it very different. I mean, they're very closely related.
Parampreet Singh: Well, they are who they are. Well, they are closely related only in the classical theory. Well, if you will go near the bounce. This will give very different effects, um,
Edward Wilson-Ewing (UNB): Well, I mean, in both cases, we have the same Ubar framework, right. I'm not choosing new barn one case and you're not in something else. I mean, these are
Parampreet Singh: The different
Parampreet Singh: So your lettuce is different, even if you are choosing the same new bar your lettuce lettuce structure is changing the other single
Edward Wilson-Ewing (UNB): Why is that, sorry.
Parampreet Singh: Because this seems to give you a different angle than the other one.
Edward Wilson-Ewing (UNB): No, because remember this is saying squared.
Edward Wilson-Ewing (UNB): So sign squared will have exactly the same spacing sign times cosine
Edward Wilson-Ewing (UNB): That's the argument that can be in your middle polling make to precisely to make this choice.
Parampreet Singh: And I might not
Parampreet Singh: Like I hope I'm not making any mistake. But isn't this the very similar thing which is also done in the hybrid quantization when they are doing the perturbations to introduce this cosine to define the the buying the McConnell society equation.
Edward Wilson-Ewing (UNB): Um, it could be I'd have to check to to see you.
Parampreet Singh: Okay. Okay. Thanks. Thanks for the clarification.
Abhay Vasant Ashtekar: So excited. I mean, I think that confusion I maybe I'm just confused. Yeah, I think the confusion was coming because you already defined what is an x and then an x, you already chosen to be equal to minus n times be divided by gamma and then you chose be to be something
Abhay Vasant Ashtekar: So that would just give you the relation between x and then to be exactly what you wrote, except for the costs delta B or B do are the X to appear.
Edward Wilson-Ewing (UNB): Right, so I probably should have been a little bit clearer.
Edward Wilson-Ewing (UNB): Few slides back I think everybody's
Edward Wilson-Ewing (UNB): Busy here this this substitution is really for the scale or constraint. And the idea here is that you know we have some
Edward Wilson-Ewing (UNB): Coming from lukewarm cosmology. We have some field strength. We want to evaluate it by going around the loop.
Edward Wilson-Ewing (UNB): And when you have a spatial curvature. It's hard to go around the loop. But you say, Okay, let me just take the transport in one direction.
Edward Wilson-Ewing (UNB): And that leads to this type of substitution. And so I'm just taking the exactly the same framework that we use in LTC and then applying it here.
Edward Wilson-Ewing (UNB): In LTC usually we don't include a lapse. Sorry, we don't include a shift vector we just set that equal to zero. And my point here is that we shouldn't
Edward Wilson-Ewing (UNB): Just assume that we're going to do exactly the same substitution to relate those two things.
Edward Wilson-Ewing (UNB): Instead,
Edward Wilson-Ewing (UNB): What we're doing here is we're saying, Okay, we have this constraint algebra, and I'd like to make it look as much as possible at the classical one and is there a way to do that. And the answer is yes. And it's through this relationship here.
Abhay Vasant Ashtekar: But I guess statement is that in going from the classical theatre effective equations you met two assumptions, one has gays fixing and one is this an X right now and to have a contradiction with each other unless cause of delta V or X multiplier Ibiza, good one.
Edward Wilson-Ewing (UNB): Um, well, I'm not sure they're in contradiction.
Edward Wilson-Ewing (UNB): I mean, there's a choice that has a need, right, because if if I have if I have this relation
Edward Wilson-Ewing (UNB): Right and the classical theory.
Edward Wilson-Ewing (UNB): How can I want to be able to
Edward Wilson-Ewing (UNB): Could say okay, I want to
Edward Wilson-Ewing (UNB): Promote this to something to where I can say, okay, what is this in the quantum theory, I have to make some choice here.
Edward Wilson-Ewing (UNB): And I agree there's a choice to be made. Right. So there's some freedom and how you do it. But if I want to promote this relationship 20 quantum theory have to do something here. Yeah.
Abhay Vasant Ashtekar: I understood
Abhay Vasant Ashtekar: One other question. Good. So yeah, let's see. So can you go back to the next. The next slide that you are using
Edward Wilson-Ewing (UNB): This one.
Abhay Vasant Ashtekar: The one that you are actually short showing not. I just know with the
Abhay Vasant Ashtekar: Next equal to minus and I'm the concert. Yeah, that one up here so
Abhay Vasant Ashtekar: Yeah, so the point is that
Abhay Vasant Ashtekar: So you achieving and is always positive. And next can be both positive and negative. Is that what is that
Edward Wilson-Ewing (UNB): Yes, that's right. Yeah. OK. OK. OK.
Parampreet Singh: OK, and maybe like I can make one final comment like because like it has really very much clarified what I was asking so
Parampreet Singh: You see, like, I can understand, like, if you do the extensive curvature quantization or the key quantization. Then you got this be to sign
Parampreet Singh: Lambda be kind of a thing. But the main question is who gives us this relation between x and n this is essentially a zoom and
Parampreet Singh: natural thing to assume would have been knowing you understand technical difficulties. I'm not objecting to this stuff.
Parampreet Singh: But naturally one would have assumed that what we assumed what we considered for be going to sign lambda be, I don't know whether it was derived or put put as a thumb rule, we should use
Edward Wilson-Ewing (UNB): So so so the
Edward Wilson-Ewing (UNB): So this, this is
Edward Wilson-Ewing (UNB): Derived that exists exactly the same level as the LTC Caleb quantization.
Parampreet Singh: Okay, so it was the right
Edward Wilson-Ewing (UNB): Exactly the same level. Yes.
Parampreet Singh: So the natural thing to do would be that if there is a relationship between x and and we would just plug in this be
Parampreet Singh: But right now, you're saying that, well, we'll let us look at the different markets and constraint and the structure of the lattice motivates that
Parampreet Singh: If I would have chosen and next exactly guided by what you did earlier as a calculation, then I will be in a mess. I won't be able to do the for the computation. So I should use a different polymerization for be here, right. So, that is what is the confusion which are ban high yet.
Edward Wilson-Ewing (UNB): Right, so what what I'm saying here is that we have two places where we have to, I mean polymer eyes be to have a theory which then we can promote to a quantum theory.
Edward Wilson-Ewing (UNB): And for the scanner constraint and falling exactly the same procedure hasn't lukewarm cosmology and for the relationship between the laps and the shift.
Edward Wilson-Ewing (UNB): There is no guidance from the club cosmology, right, because they're the shift is always zero. So what do I use for guidance. Instead, I tried to mimic the structure of this constraint algebra as much as possible.
Edward Wilson-Ewing (UNB): But
Parampreet Singh: You would agree right there is a multitude of choices.
Edward Wilson-Ewing (UNB): Once you give up that little late. Absolutely. There's a
Parampreet Singh: Multitude of choices and there is only one fine tune choice which gives you what you are asking for.
Edward Wilson-Ewing (UNB): Well, any choice is fine tuned mean if you make a choice, right.
Edward Wilson-Ewing (UNB): You're picking something. Yeah.
Abhay Vasant Ashtekar: I think I think what he's saying is that in the effective theory right if I just look at the space level. I just have one constraint, because you have fixed the different models of constraints disappeared. Right.
Abhay Vasant Ashtekar: There's only one constraint and so they affect the city, you can forget about this an x is equal to, blah blah blah, that we got up here, right, this relation that is at the bottom of the transparency.
Abhay Vasant Ashtekar: And the level of the face face. I don't need to know what is an x, because it's so what Eddie saying is that at the level of face to face, and just rephrasing what is it I'm sorry but to
Edward Wilson-Ewing (UNB): Go ahead please.
Abhay Vasant Ashtekar: And so what he's saying is that
Abhay Vasant Ashtekar: At the face base level. I don't have to say anything about annex so he has chosen that be by the
Abhay Vasant Ashtekar: By the
Abhay Vasant Ashtekar: Key alanna me and that is the end of it, and you can just solve the problem at the space level and I'm acted, but there is still a second issue, which is that you're got some trajectory in the face space. And how do you connect them to the space time metric
Edward Wilson-Ewing (UNB): Right.
Edward Wilson-Ewing (UNB): And, you know,
Abhay Vasant Ashtekar: And he's saying that, well, logically, this is an independent choice.
Abhay Vasant Ashtekar: And it is, it can be made in order so that the cluster algebra is exactly that. I mean, somebody might argue and say that, well, no. I mean, you can just let the costs of delta be
Abhay Vasant Ashtekar: Delta is be or x
Abhay Vasant Ashtekar: As it is, so that the constraint algebra has a slightly modified with the classical you make you get the right answer, but he put in. I mean, this is a choice. And as I had said let's see what happens with respect to the choice.
Edward Wilson-Ewing (UNB): Yeah.
Edward Wilson-Ewing (UNB): Okay, um, let me continue because I, I would like to get through a few other things. Um, so anyway, so this is
Edward Wilson-Ewing (UNB): The
Edward Wilson-Ewing (UNB): Effect of three. I'll be using
Edward Wilson-Ewing (UNB): So this is the
Edward Wilson-Ewing (UNB): Effect of scale or constraint. This will give me the equations emotion which we can solve. And then from once we have solved the equations emotion, then we can reconstruct
Edward Wilson-Ewing (UNB): The space time and in part to use this to figure out what the shift factories. When we get the metric. Okay.
Edward Wilson-Ewing (UNB): So if we look for a stationary solution we can solve the effective dynamics explicitly analytically for pain Libby goals friendly coordinates where we set the shift equal to one and that gives this metric here.
Edward Wilson-Ewing (UNB): And here RS is equal to is just a short short radius of to GM the classical social radius.
Edward Wilson-Ewing (UNB): Okay, um, as you can see right away. This solution is only valid for x greater than some minimal value just because you have this square root. And if you want to make sure that the square root of this as well defined. You need to make sure the x is greater than this X Men.
Edward Wilson-Ewing (UNB): This X Men lies well within the short short radius.
Edward Wilson-Ewing (UNB): And I want to stress that, of course, this is one solution that we get for payment, the goals around like coordinates.
Edward Wilson-Ewing (UNB): You can make other choices for the laps. And one thing that we did is that we wanted to make contact with results by Gambino meadow and Poland, and so we also
Edward Wilson-Ewing (UNB): Checked setting the labs equal to this, which is what they, the choice that they made and their paper and we get exactly what they get.
Edward Wilson-Ewing (UNB): So there's a nice concordance of results here. So if you if you follow their approach, which is really to villainize the constraints or if you follow our approach, which is to gauge fix
wolfgang wieland: Then at the end of the day that
Edward Wilson-Ewing (UNB): You get these two results which match.
Edward Wilson-Ewing (UNB): Okay. And I want to go through the details of this FaceTime, one by one by do want to mention a few important points. So the first one that I thought was interesting.
Edward Wilson-Ewing (UNB): Is that if you have a mass a black hole or in quotation marks here black hole with a mass which is less than the plank mass, there is no horizon.
Edward Wilson-Ewing (UNB): So if you want to get a horizon, you need a mask greater than the plank last and here when I say horizon. I'm just talking about a killing horizon.
Edward Wilson-Ewing (UNB): Okay, so that's the first point. The second point is that this solution has on our horizon and also inner horizon. So if you have, you know, a large black hole, you'll have an outer horizon.
Edward Wilson-Ewing (UNB): Here we're late concepts over
Edward Wilson-Ewing (UNB): This is essentially at the classical value of the short short radius. There are some small corrections which her you know quite suppressed.
Edward Wilson-Ewing (UNB): By for at least for a large black hole. And you also inner horizon. When the light cone tips over again. And then in between X Men and X, enter your, your particles move both in words and opens
Edward Wilson-Ewing (UNB): And here, this gray region is the region, which were the solution just doesn't exist.
Edward Wilson-Ewing (UNB): And finally, the curvature and variants are bounded and I've given the their balance here um this result isn't so surprising because we've cut off the space time. You can't get to x is equal to zero here. So this is nice, but perhaps not.
Edward Wilson-Ewing (UNB): Super convincing at this stage because really, we've just cut off the space time here.
Edward Wilson-Ewing (UNB): Okay, so this is what we get. We look at the vacuum solution.
Edward Wilson-Ewing (UNB): And
Edward Wilson-Ewing (UNB): In some ways is quite nice. We see that we get some quantum gravity effects exactly in the region where we would expect this is exactly
Edward Wilson-Ewing (UNB): So this region here is exactly the region where the freshman curvature is of the Planck scale. So these curvature effects turn on exactly where we want them to
Edward Wilson-Ewing (UNB): The effects at the horizon are miniscule very, very small. They're essentially suppressed by
Edward Wilson-Ewing (UNB): The array gap divided by the shore shield radius squared. So the effects of the horizon are very small and they turn on exactly where we expect them to be where the Christian Skylar according to GR would reach the Planck scale.
Edward Wilson-Ewing (UNB): Okay, but there is a problem in that this region here just we don't have a solution for that space. I'm just kind of ends sharply.
Edward Wilson-Ewing (UNB): And
Edward Wilson-Ewing (UNB): That is
Abhay Vasant Ashtekar: Very
Abhay Vasant Ashtekar: Good. So is that a Kobe just singularity, or what. What does it mean to say it ends or there's a metric become complex or
Edward Wilson-Ewing (UNB): The metric becomes complex
Abhay Vasant Ashtekar: Microbiome complex. So,
Edward Wilson-Ewing (UNB): If we look here, this term here becomes negative.
Abhay Vasant Ashtekar: Okay.
Carlo Rovelli: Ed.
Edward Wilson-Ewing (UNB): Yes.
Carlo Rovelli: I'm confusing. Once again, the this again. The, the doubling of x and the side effects. What happened is in the selection solutions that we have been studied the effective solutions is that if you follow x
Carlo Rovelli: Namely, the, the area of this year's you come from large, you get to a minimum size.
Carlo Rovelli: And then the space time continues and and the girls again. So there is no
Carlo Rovelli: There's no region of space time with x less than some x minimum. But that's not the end of the world. So just that continues.
Carlo Rovelli: I mean, you can have a model that shrinks and gets the minimum and then opens up so you can have a
Carlo Rovelli: I'm just on the one hand, it seems that this is very similar to the geometry that we have. But the other hand, you seem to be describing differently is saying that something stops there, and especially that x is unique because in
Carlo Rovelli: In if you get if you go to this page fixing that you started the very beginning was a G. Geez, x squared.
Carlo Rovelli: Then x has the two points in space time we're access same value and they connected smooth three so so Max minimum or you just catching this possibility out a priori or no. Is it what what's going on here. It's me, confusing about the geometry.
Edward Wilson-Ewing (UNB): Um, maybe I think it might be easier if I continue a little bit
Edward Wilson-Ewing (UNB): And we'll see what happens when I add matter.
Edward Wilson-Ewing (UNB): Okay, so I'm not going to just rule out that there could be some, you know, perhaps surprising geometries that come out here. But in any case, at this stage, my first instinct was okay we need to add matter.
Edward Wilson-Ewing (UNB): And we were able to do that. And we got some quite interesting results, which I think will will address your questions and if they don't, please come back to that.
Parampreet Singh: Can I ask a question.
Parampreet Singh: Yes, please. So what happens when I said perfect share. Is it is it bounded or
Edward Wilson-Ewing (UNB): Um, yeah, so that should be captured in the question Skyler and and that will be bounded here. But of course, we're only going up to X Men here.
Parampreet Singh: Know what
Parampreet Singh: But you could compute your sigma square right
Edward Wilson-Ewing (UNB): Yeah, I don't think we did that, but I would expect it to be bounded, but I don't think we did the calculation.
Okay, thanks.
Johannes Münch: I have another question.
Edward Wilson-Ewing (UNB): Yes, please.
Johannes Münch: Um, I would also comment on on what Carlos said basically, I think the choice of gauge already basically exclude the possibility of bounce here, right, because usually this bouncing balls, you have this error rate is as a function of a parameter. And you see that the derivative can zero
Johannes Münch: At the bounce. So you cannot so so this function has essentially two branches and you cannot inverted because
Edward Wilson-Ewing (UNB): Well, I think, I think this is based on looking at the Kentucky sex space time where you're really viewing it as some sort of cosmological
Edward Wilson-Ewing (UNB): Model, where the value of the scale factors tells you how big the space time is here. I want to be able to describe the interior and exterior and I would like to be able to you know put an observer at any value of x. At any instance of time.
Edward Wilson-Ewing (UNB): And so here, x is just
Edward Wilson-Ewing (UNB): Increasing as you move outwards.
Johannes Münch: Yes, I'm fine with this so might my let me rephrase extra
Johannes Münch: So is actually the second solution to your equations which might be due to different choice of the science somewhere which you might lose X Men to to your current solution where you can interpret one as the black home branch and device as the white one branch.
Right.
Edward Wilson-Ewing (UNB): I
Edward Wilson-Ewing (UNB): Don't think so, but I'd have to check in detail.
Okay.
Carlo Rovelli: Yeah, but I would be interested in that because that's the that the geometry.
Carlo Rovelli: That we are studying so whether it, it matches with your, your way of computing it
Edward Wilson-Ewing (UNB): I think. But, but, again, let me let me add in matter because I think this will change the perspective, at least it did for me.
Edward Wilson-Ewing (UNB): But yes.
Carlo Rovelli: I mean tell me shut up. If you want to go ahead
Edward Wilson-Ewing (UNB): No, it's okay.
Carlo Rovelli: I think that the problem. What happened with the matter is is nothing to do with the problem. What happens when the
Carlo Rovelli: Small curvature is more radius is. I mean, if you if you just look at the standard. The black hole pedals diagram of the one with the singularity.
Carlo Rovelli: I mean, there's one point to a macro arrives and then there's a huge horizon. So there's a huge region where our becomes small fire very far away from Latin. So there's a problem. What happens with small are
Edward Wilson-Ewing (UNB): So,
Carlo Rovelli: Mike independent of ladder.
Edward Wilson-Ewing (UNB): Right. So my argument, and I'll be coming to this in a second is that this whole region here has to contain matter.
Carlo Rovelli: So that that excludes the models. We've been studying in my side. Right.
Edward Wilson-Ewing (UNB): Well, as far as I understand you've been looking at vacuum solutions right
Carlo Rovelli: We have global picture.
Carlo Rovelli: Matches the matter is somewhere and there's about matter bounce. But then there is a region where you just cross through the singularity far away from matter, no matter whatsoever. And you go from the tropical. Tropical region is just look at that one far away.
Carlo Rovelli: Then it's a little. It's a little Kentucky sucks. If you want, you wait for the rise on away from the, from the matter which is look there, but there is a position there without matter.
Edward Wilson-Ewing (UNB): So what we find is a little different.
Edward Wilson-Ewing (UNB): Okay. Yeah. So I think there are some similarities, which are interesting, but there are also some differences. So let me, let me try to explain
Abhay Vasant Ashtekar: I think it just is different because then I know but you know horizon, you've got all these things which which was which all these effective space times that in a web in considering coverage because it in don't have these you know horizon is a completely different global structure.
Yeah yeah
Edward Wilson-Ewing (UNB): Okay, so for for us, at least when we, when we got this. We thought, okay, maybe we should add matter and see what happens in that case.
Edward Wilson-Ewing (UNB): Are we able to fill this hole or is there or should we look for something else entirely different, but if we add matter what happens.
Edward Wilson-Ewing (UNB): Now, we had some motivation behind this. I want to explain the motivation and this very is very much a hand waving argument.
Edward Wilson-Ewing (UNB): But what's nice is that we'll see in just a little bit that this hand-waving argument becomes very precise. So if we have a gravitational field. Let's say black hole.
Edward Wilson-Ewing (UNB): Normally we would say, okay, well, there has to be some sort of sort of source now hysterical symmetry. We don't have any gravitational waves. So the only source possible ism is
Edward Wilson-Ewing (UNB): Now, classically, of course, you can just say, okay, we put my mass at the origin. And I have some delta function source.
Edward Wilson-Ewing (UNB): But if you think from porn gravity and say, look, quantum cosmology that you could have an upper bound on the density of your matter field.
Edward Wilson-Ewing (UNB): Of the Planck scale, then that means that if you have a compact object of some mass capital M, it has to have some extent. And specifically, it has to extend at least to a minimum radius given by this mass divided by maximal density and taking the cube root. And if we look at what happens.
Edward Wilson-Ewing (UNB): Here. Sorry for X Men, that is exactly where this shows up.
Edward Wilson-Ewing (UNB): So this suggests that maybe matter plays an important role here.
Edward Wilson-Ewing (UNB): Okay, but I want to stress this is just a hand waving argument to motivate this
Edward Wilson-Ewing (UNB): So to explore this, what we did is we added
Parampreet Singh: Some question.
Edward Wilson-Ewing (UNB): Yes, please.
Parampreet Singh: Okay, so I have some issues with all this arguments. The point is, like, first of all, it gives us who gives us this our bond roll less than Rafi
Edward Wilson-Ewing (UNB): So prompt. This is just motivation.
Parampreet Singh: Okay, but I'm just
Parampreet Singh: I'm here. I don't know when he started regularly. So I will make this precise in a minute, but at this stage is really just to motivate
Edward Wilson-Ewing (UNB): Heading matter if you think that the argument is week. That's okay.
Parampreet Singh: No, no. Well, let me just ask my question first point is that even if you have rule, less than Rosie, even if you assume that like
Parampreet Singh: From el que se that maybe that could occur. And if you asked arguments. Okay, let us look at the Yankee one, for example, they are also
Parampreet Singh: Row was less than Rosie, but the main role played in the space times even if the matter is present is by a nicer trapeze. We know that. So you will never reach row close to Rosie and your X Men, even with the same argument will be very large.
Edward Wilson-Ewing (UNB): Sure. So what that means is that this if you include some and I saw trapeze or something else, then what you're essentially doing is you're making this even bigger.
Parampreet Singh: No, you don't have to include a nicer properties are already there.
Abhay Vasant Ashtekar: Sure.
Abhay Vasant Ashtekar: If but if you apply that in the argument.
Edward Wilson-Ewing (UNB): This makes this even bigger.
Edward Wilson-Ewing (UNB): Right, because you're making row smaller, so you're making you know this whole thing together bigger. So you're saying that actually we need to include matter even further up
Parampreet Singh: Absolutely, yeah.
Edward Wilson-Ewing (UNB): So, so yes. Either way, um, it really suggest that we should include matter to try and understand what's happening here, at least, and I, again, I don't want to spend too much time on this because it's not a central point. This is just, you know, a motivational argument.
Parampreet Singh: No, but I think it's an important point. So let me just summarize the technical points so far. So the point is, like, we made certain good choices.
Parampreet Singh: We did K quantization. We then meet certain choice of Annex and an end. We ended by saying, well, now if I do not include matter, things don't work. My metric becomes complex below X Men, so I should go back to the square one and redo the analysis with matter. Isn't that what we're doing.
Yeah.
Edward Wilson-Ewing (UNB): And again, so. So this is just, you know, motivation and
Edward Wilson-Ewing (UNB): I'm going to make it precise in a second and how this argument really does work.
Edward Wilson-Ewing (UNB): In more detail. And so what we did is that we added a dust field. Um, we use the dust time gauge which means that we set
Edward Wilson-Ewing (UNB): We, we, we use the dust field as the clock and this sets the laps equal to one this is on top of the arrow gauge, of course. And then we get a true Hamiltonian
Edward Wilson-Ewing (UNB): And the equations emotion or essentially the El que or some version of El que je effective equations for LTV space times in panel of eagles friendly coordinates. And when I say Pelham eagles turn like whereas I just mean that the lapses equal to one.
Edward Wilson-Ewing (UNB): Okay, so here is the true Hamiltonian after we've added the dust field and we use it as a relational clock.
Edward Wilson-Ewing (UNB): Of course, it's no longer constrained right this is a true Hamiltonian and the energy density of the dust field is related to the value of this effective Hamiltonian
Edward Wilson-Ewing (UNB): Um, let me go through this quickly because it's not so important we get some equations emotion their exact form is important. The point is, I want to show you that we have equations emotion for general LTV space times
Edward Wilson-Ewing (UNB): But what we do. We don't. I mean going and solving all the LTV space times. Is it a little ambitious to start. So we said, Okay, let's just look at the simplest model that we can think of, which is open hammer Snyder collapse.
Edward Wilson-Ewing (UNB): And so this is a star of some radius L and L is dynamical right so we have a star which is going to collapse. So l will get smaller and smaller.
Edward Wilson-Ewing (UNB): And the energy density of the dust field is zero outside of the star and it's constant inside. And of course, as the star collapses this density will increase. So the question is what happens dynamically
Edward Wilson-Ewing (UNB): Now we can take the LTV equations emotion and apply it for this system and see what we get. So what I'm going to tell you. Next is not something I'm putting in by hand but it's a derivation of these results from the LTV equations here.
Edward Wilson-Ewing (UNB): And so this is the equation that we get for how L evolves and as you can tell this is exactly the effective Freeman equation for LTC so it seems to me a very nice convergence of ideas where we're applying the same methods that we do and lukewarm cosmological spherical cemetery.
Edward Wilson-Ewing (UNB): And this gives us some very general equations for LTV space times. But if we apply it in a context where you would expect the QC equations to work.
Edward Wilson-Ewing (UNB): And of course the open hammer Snyder model is exactly such a case, because the interior modeling as a space with a homogeneous space.
Edward Wilson-Ewing (UNB): than you'd expect to recover the LTC equations emotion that's exactly what we get. And what I want to stress is that we get everything exactly the same, even the value of the critical energy toasty here in matches exactly with LPC
Edward Wilson-Ewing (UNB): Okay, we can also find explicit solutions for all of the other terms. I'm not going to show that here. I'll just refer you to the paper. If you're interested in the details.
Edward Wilson-Ewing (UNB): But what we see is that there's events. So you have a star, it collapses, it reaches a minimal radius. And then it bounces up
Edward Wilson-Ewing (UNB): Now,
Edward Wilson-Ewing (UNB): Another interesting thing, and this is where I'm making precise what I put the hand waving argument I gave earlier.
Edward Wilson-Ewing (UNB): Is that you can solve for the radius of the star Lt. And you can see, okay, what is this minimal value and it's minimal value turns out to be exactly X Men, where the vacuum solution ends so
Edward Wilson-Ewing (UNB): The way that I interpret these results. Is that your vacuum solution goes up to a point.
Edward Wilson-Ewing (UNB): And inside that point, you need matter. But if you include matter, then you're guaranteed that your solution will extend at least that far. So of course before when you start. It's big and it's just starts to collapse.
Edward Wilson-Ewing (UNB): It's much bigger than X Men, but the smallest point it reaches is X Men and then it bounces back out again.
Parampreet Singh: It can make a very small point
Edward Wilson-Ewing (UNB): Yes, please.
Parampreet Singh: Isn't this coincidence, precisely because of sorry I won't say like, this is a coincidence, precisely because of we are working with a K quantization.
Parampreet Singh: And you did exactly the same polymerization, which led to the X Men similar polymerization, which is done in elk. You see what especially flat model. And if you would have chosen to include spatial curvature in quantum gravity affects then this coincidence will not offer
Edward Wilson-Ewing (UNB): Right. So here I agree, we have to keep in mind that we're we're comparing apples with apples and we're doing the same Luke quantization. So if, if we were to do
Edward Wilson-Ewing (UNB): As you say, let's say in a loop quantization, then you may not expect them to match because there are some quantization ambiguities. But my point here is that, at least to me.
Edward Wilson-Ewing (UNB): It was surprising that we do this in spherical symmetry and we get some very general equations and then we reduced down to this case we get exactly what we would have gotten admittedly following the same quantization procedure, but still we get exactly the same thing.
Edward Wilson-Ewing (UNB): No, but I would have expected. Maybe some small corrections, but that doesn't even happen here.
Parampreet Singh: Nobody but the point is, like, once we assume the aerial cage and once we take the cake quantization, we are essentially in the same system.
Edward Wilson-Ewing (UNB): No, no, no, no, no, no.
Abhay Vasant Ashtekar: This, this particular metric is completely different system.
Parampreet Singh: Know, obey. That is, it is true. It is true, it is asparagus metric. It's a completely different system, but the quantization effects are essentially what are done in specially flannel QC
Edward Wilson-Ewing (UNB): Well, I mean, I'm following the same procedure. I agree. I mean, the whole point here is to use the same input and then see you know do we get something that comes out, which is consistent right
Edward Wilson-Ewing (UNB): I'm definitely not
Edward Wilson-Ewing (UNB): Building everything from scratch and become very much using work that's been done before. There's no question
Suddhasattwa Brahma: But here.
Edward Wilson-Ewing (UNB): I mean, classically, I have all these quantities that depend on x, right, everything has an x dependence, right, if you look at the equations of motion. Here I have all these spatial derivatives here in here.
Edward Wilson-Ewing (UNB): Right, so the fact that, then when I look at some limit where I have a homogeneous matter field I recover exactly the same.
Edward Wilson-Ewing (UNB): Equations emotion I, for me, it was, it was a nice result.
Abhay Vasant Ashtekar: Not by me. This got totally unexpected so i don't i don't think it is that something that I would have seen it just from the metrics, you're using. So
Suddhasattwa Brahma: Can I ask a quick question. This is true, though.
Suddhasattwa Brahma: So it's so if just to build on this question. If you include special curriculum shouldn't expect equals one cosmology. If you're really doing Oppenheimer Snyder for the interior like wouldn't expect that effect to be, I mean, forget
Edward Wilson-Ewing (UNB): Yes, you're right.
Edward Wilson-Ewing (UNB): So here I haven't studied that yet because there's so much to be done here. I mean, here I'm giving you what we've done so far. And there's a lot to be done.
Edward Wilson-Ewing (UNB): Here I made a choice here just to simplify things, and I chose that Eb is equal to x. So that's a choice that you can make when you're looking for a certain solution.
Edward Wilson-Ewing (UNB): And then that corresponds to the flat.
Edward Wilson-Ewing (UNB): Open hammer cider.
Suddhasattwa Brahma: Yeah. Thank you. Yeah.
Edward Wilson-Ewing (UNB): So you're right.
Edward Wilson-Ewing (UNB): I would be interesting to see what happens if we put in
Edward Wilson-Ewing (UNB): Another choice which would give something that
Suddhasattwa Brahma: Would be closed. Yeah.
Parampreet Singh: And I think like just to add to both of your commands like Adams and and and Romans comment like first like to. I was. I didn't meant to say like the system. The same. But I thought you understood, like what I meant like the condition procedure, the main steps.
Parampreet Singh: Of similarities
Parampreet Singh: The second point was like
Edward Wilson-Ewing (UNB): Sorry if I misunderstood you I hear, I agree that the quantization steps are very similar. I mean, very much followers
Parampreet Singh: But just
Parampreet Singh: To just to clarify the word
Parampreet Singh: For bromance. Like if one has to include key code one in this case, then the right quantization to do will be the A quantization. In the first step, not the key quantization to make to repeat the similar arguments.
Edward Wilson-Ewing (UNB): While you could do either. Right. And then you could compare with the K or the a little quantization.
Parampreet Singh: Yeah, but then you won't get you won't get the agreement, what you have, if you do K and then k equal to one here.
Edward Wilson-Ewing (UNB): Um,
Edward Wilson-Ewing (UNB): I'm not sure. I mean, it's certainly possible. Yeah.
Edward Wilson-Ewing (UNB): Okay, so. So what we find in this case is that we get a bounce.
Edward Wilson-Ewing (UNB): And
Edward Wilson-Ewing (UNB): And what we really have is we have some collapse or we have a collapsing star it reaches a minimal radius. And then it starts to bounce back up.
Edward Wilson-Ewing (UNB): Okay. And here, um, this model really gives us, I think, a very nice and explicit realization, but transition from a black hole.
Edward Wilson-Ewing (UNB): To and here and being very careful what I say something which isn't some ways similar to a white hole which is generated by quantum gravity effects.
Edward Wilson-Ewing (UNB): And also, as you notice that the title I have white hole in quotation marks.
Edward Wilson-Ewing (UNB): So why am I doing this. Why am I not seeing away whole. Well, the reason is it's not exactly a white hole. There are some very important similarities but it's not a white hole as you would see in the classical GR textbook. So the reason for that is that if you look at the space time
Edward Wilson-Ewing (UNB): Someone who's outside doesn't notice
Edward Wilson-Ewing (UNB): What's happening inside. So here, if you're if you reach the outer horizon, right, which is essentially the sword shield radius for large black hole. This is still a trap surface.
Edward Wilson-Ewing (UNB): So an observer in here is moving towards the left. This is still trapped the differences inside the star which here I'm showing in grey you have observers, which are anti trapped. So you have a sort of white hole like region here.
Edward Wilson-Ewing (UNB): But this part still looks like a black hole.
Edward Wilson-Ewing (UNB): So in some ways, you have the similarity with white hole, but it's not a white whole space time at all.
Edward Wilson-Ewing (UNB): And of course as the system evolves. After the bounce rate. So you have your, your star which collapses and bounces in the balls outwards. So, then your
Edward Wilson-Ewing (UNB): Radius of this matter field is slowly moving outwards and once it passes the outer horizon there won't be a black hole anymore in the sense that there's no longer under horizon.
Edward Wilson-Ewing (UNB): Okay, so this is the general picture of what's happening.
Edward Wilson-Ewing (UNB): I'm almost out of time. So let me just quickly say a few things about this.
Edward Wilson-Ewing (UNB): I showed you some explicit
Edward Wilson-Ewing (UNB): Equations. So some explicit analytic solutions for
Edward Wilson-Ewing (UNB): I couldn't show them to you. But in the in our paper we have some explicit analytic solutions for
Edward Wilson-Ewing (UNB): If we go back here for Eb be an annex, and this is explicit solutions for the open hammer slider model.
Edward Wilson-Ewing (UNB): Now, when we do this we're neglecting these edge effects at x is equal to L and that's perfectly fine, because in the open hammer Snyder model as it collapses all the fields are continuous. They're not necessarily differentiable at the boundary, but they are continuous now.
After
Edward Wilson-Ewing (UNB): After the bounce. What you see here is that you have an anti trap region here and attract region here and there's clearly a discontinuity between the two.
Edward Wilson-Ewing (UNB): So what that means is you have to include these edge effects. Now, so that means that, okay, we had some nice solutions which were very simple for the pre bounce. But after the bounce. We have to be a little more careful.
Edward Wilson-Ewing (UNB): And in particular, you can check that this be here is discontinuous at x is equal to hell.
Edward Wilson-Ewing (UNB): And so to understand how L moves outwards. We can't just use the open hammer Snyder equations anymore. We have to use the full LTV effect of equations.
Edward Wilson-Ewing (UNB): Okay. And these of course are a lot harder to solve.
Edward Wilson-Ewing (UNB): So I won't go through the details here, but if you just do a back of the envelope calculation. This suggests that this discontinuity really slows the expansion of this wave front.
Edward Wilson-Ewing (UNB): And it suggests that the lifetime of the black hole would be around M squared over and plank. Now this is a very rough back of the envelope estimation. So we really need to do further work To check to see if this is correct or not. But this is what the first
Edward Wilson-Ewing (UNB): First explorations indicate and I just want to mention here that when I talk about the lifetime of a black hole. I'm assuming that both the formation of the black hole. So you have a collapsing star, presumably, that's an energetic event. And then when the
Edward Wilson-Ewing (UNB): The wave front comes out again. That's also an energetic event that will send out photons.
Edward Wilson-Ewing (UNB): So I'm saying, Okay, we have some distant observer. That's really far away and he sees some photons that are emitted as the star collapses and forms of black hole and then you see some photons again when the way in front
Edward Wilson-Ewing (UNB): Of the matter field reaches the horizon, or just passes the horizon and more photons are emitted and so he's measuring the time between the photons that he receives from the collapse and then from the expansion from a distance. That's very far away.
Edward Wilson-Ewing (UNB): Okay.
Edward Wilson-Ewing (UNB): So I'm almost done. I just want to say a few things about the ramifications for the information last problem. So if this is the correct lifetime.
Edward Wilson-Ewing (UNB): Then I think this would have some quite interesting ramifications for the information loss problem. So first, we don't have any singularity. So there's no no place for information to just
Edward Wilson-Ewing (UNB): You know, and or be lost entirely and there's no eternal event horizon, behind which information can just hide forever. So those are two places where people sometimes think, oh, this is one way that information loss could happen. Well, these just aren't available in this space time
Edward Wilson-Ewing (UNB): Now, on top of that people often argue that the potential information loss becomes a real problem after half of the black hole has evaporated.
Edward Wilson-Ewing (UNB): And the idea is that, okay, you have a black hole and you have some hockey radiation and as hockey radiation goes on.
Edward Wilson-Ewing (UNB): You'll have some entanglement between the hockey radiation what's left of the black hole.
Edward Wilson-Ewing (UNB): And this is fine until all of a sudden, there are more degrees of freedom in the hotkey radiation and in the black hole.
Edward Wilson-Ewing (UNB): And then you would expect that you'd have to have some purification for the entertainment entry to decrease since the
Edward Wilson-Ewing (UNB): number of degrees of freedom in your black hole is getting smaller and smaller.
Edward Wilson-Ewing (UNB): And the page. Time for a black hole. If you just look at the standard quantum field theory calculation would be MQ over m squared.
Edward Wilson-Ewing (UNB): So if the black hole lifetime, because we calculated here is only M squared over and playing so much shorter
Edward Wilson-Ewing (UNB): Then this would say that the Hawking evaporation process is a sub leading quantum fact, of course, it's still there, but it's just much slower and there's not enough time for information loss to become a problem in this case.
Edward Wilson-Ewing (UNB): Okay, I'm out of time. So let me just conclude very quickly. So what we did is that we drive some LPG effective equations with hello on me corrections for
Edward Wilson-Ewing (UNB): For strictly symmetric space times, both in vacuum and with a dust field.
Edward Wilson-Ewing (UNB): In vacuum. We get solutions that agree with what was found by can be neoliberal in Poland, following the different approach. So I think this is quite nice. We have these different approaches that give the same result.
Edward Wilson-Ewing (UNB): We find an enterprise and also minimum radius, where the vacuum solution breaks down.
Edward Wilson-Ewing (UNB): So then we added a dust matter field. And not only can we know describe the entire space time there is no minimum inner you know X Men were the solution, because then I can go all the way down to x equals to zero.
Edward Wilson-Ewing (UNB): And what happens is I have a collapse. I have a bounce and then as it comes out. I have a shockwave and as I just finished saying we estimate the lifetime of the black hole to be m squared over complaint.
Edward Wilson-Ewing (UNB): Okay, um,
Edward Wilson-Ewing (UNB): Let me just put up some open questions. Of course there. There's a huge number of things that still need to be explored. And these are just some of them. It's some of the ones that I've been thinking about the most. But it's by no means an exhaustive list or tons of other ones.
Edward Wilson-Ewing (UNB): So thank you all for listening.
Carlo Rovelli: I have a question.
Edward Wilson-Ewing (UNB): Well, please.
Carlo Rovelli: So in 2222 comments, more, more than questions I had that this is this is very nice. Thank you very much. I mean, very solid. As always, when you do things the first comment is about em square
Carlo Rovelli: It's just, I mean I'm I'm super happy of seeing and square coming can can be coming back because m square. I mean, then the lifetime of box goes whole n square
Carlo Rovelli: It's a, it's a possibility, how and I pointed out that there's just a dimensional hand waving argument that says that it is possible on quantum gravity dimensional argument that things happen and square
Carlo Rovelli: And so
Carlo Rovelli: It was a it was a, we were very excited because, of course, there is a
Carlo Rovelli: There's other phenomenology. That could be related to him square. I mean, for Jessica has explored that there is even some some astrophysical search for em square phenomenon and black holes.
Carlo Rovelli: Primordial black holes exploding today if if the lifetime is I'm square could give a good give up several things. So it's fantastic and very happy that this is reinforced I was losing hope of em square
Carlo Rovelli: Because of spin form calculations that were saying, No, no, no. It says, It's too early for for something to happen when you look at the at the quantum gravity horizon.
Carlo Rovelli: But I want to. So recently I was just, you know, thinking no no no black holes are going to stay there, all, all VM in Cuba life.
Carlo Rovelli: But, but, but it's nothing solid in in in our results in fact i i from, from the point of us being forms. I think it's a
Carlo Rovelli: There are indications from Cuba, but but but it would be fantastic on for quantum gravity and for for observations, if they were MS clear phenomena, but that's the first comment. The second comment is that yeah i mean
Carlo Rovelli: By put it very clearly that the kind of model. You're doing it differs from a transition across the
Carlo Rovelli: The Singularity without Makar that has been exploring in various ways in in in other ways.
Carlo Rovelli: But, but, you know, but but God is complicated. And then of course the, the choice of of coordinates in which we are kind of make things very, very, very, very different. So
Carlo Rovelli: I think
Carlo Rovelli: I'm particularly impressed by your matter part and by the appearance of this pseudo pseudo
Carlo Rovelli: HTC
Carlo Rovelli: Friedman equation that we appears here that that that's very surprising and the fact that it can be described the bounce the bounce. It's remarkable perhaps
Carlo Rovelli: Perhaps things could stay together if if we look, I would like to see
Carlo Rovelli: Somehow the full in a pot is is on the basis of that of the full space time. I mean, the full Council structure of the space time that comes out, comparing with a one that comes from other from other analysis, then we do these things is not. I mean, I understand that.
Carlo Rovelli: Understand the beauty of doing rigorous system that some simplification that you can
Carlo Rovelli: That you can do exactly understand the strength of that, of course, very well. But, but at the end of the day, physicists complicated. I mean,
Carlo Rovelli: Black was a complicated thing there is a star that collapses. There's a part that bounces. There's a you can go get to the singularity far away from the star days arise. So there's a lot of pieces. And it seems to me that each one is treated in an approximation.
Carlo Rovelli: And we have to be flexible enough to see the various it's about pick up the right hint from each one of these models that the second, the second comment.
Edward Wilson-Ewing (UNB): Yeah, and I agree with both. And let me just add one other comment. I think that, you know, there's a lot of things that are going to be explored right i mean
Edward Wilson-Ewing (UNB): For even what what I'm presenting here. This is very much. You know what first few steps in this direction. And there's more to be done. And there's more to be done in other directions to mean
Edward Wilson-Ewing (UNB): The more we do it, the more the more will learn for sure. So
Carlo Rovelli: Thanks very nice, very nice presentation. Thank you.
Francesca Vidotto: Look at which one would be the first thing to do in this list of open questions in order to go ahead with this one.
Edward Wilson-Ewing (UNB): Um, well, I can tell you what I'm doing. I'm doing I'm working on the third and fourth ones.
Edward Wilson-Ewing (UNB): Um, but, you know, I think that's something that each person will have their own answer to. And I think any progress in any of these questions will be very, very helpful, but I'm personally currently working on the third and fourth
Abhay Vasant Ashtekar: Okay, so, hooray asked me to
Abhay Vasant Ashtekar: To take you to share the session because he has a class to teach. Let me see what
Abhay Vasant Ashtekar: Participate right. I think it should die as a question. So does a comment or question. Thanks.
Suddhasattwa Brahma: So kinds of a nice presentation. So my question is very related to this to this relating the last to the shift like you know you introduce this cost cosine function or not. So the first question is, if you do not include that cosine in that relationship.
Suddhasattwa Brahma: Does that affect your equations of motion. Does that affect the square root factor that comes in. Later on, which excludes part of your space for the backend system.
Edward Wilson-Ewing (UNB): Okay, so it doesn't affect the equations emotion. But what it does do is that it affects the metric that you extract afterwards.
Edward Wilson-Ewing (UNB): Because, of course, to know the metric you need to know what the shift.
Edward Wilson-Ewing (UNB): Vector is
Suddhasattwa Brahma: Yeah, that's
Suddhasattwa Brahma: The metric in a way that this region is not
Edward Wilson-Ewing (UNB): Right. So what happens actually is a little bit surprising if you just put in
Edward Wilson-Ewing (UNB): The sign but term by itself without the cosine, you just end up there's there's some cancellation that happens in unit back with the classical solution.
Edward Wilson-Ewing (UNB): So that there's certainly some ambiguity, what you want to do there. But if you make the choice of
Edward Wilson-Ewing (UNB): Of just sign of, you know, square delta be horror x divided by that.
Edward Wilson-Ewing (UNB): Then you just get back the classical solution.
Abhay Vasant Ashtekar: But how can I get back to classical solution because
Edward Wilson-Ewing (UNB): There's some cancellations. That happened.
Abhay Vasant Ashtekar: So, so all the delta goes away everything else.
Abhay Vasant Ashtekar: Yeah, it is.
Edward Wilson-Ewing (UNB): It's a little surprising. Yeah.
Abhay Vasant Ashtekar: It's not surprising be shocking.
Abhay Vasant Ashtekar: Okay.
Abhay Vasant Ashtekar: Let's see. I think this has a question.
Abhay Vasant Ashtekar: Right.
Suddhasattwa Brahma: Yeah, I'm trying to lower my hand.
Yes.
Johannes Münch: Yes, I have another question.
Please.
Johannes Münch: So this x. So you have this metro space time and you have this exterior non metro space time and the exterior space time has a column horizon. That's right.
Edward Wilson-Ewing (UNB): Um,
Edward Wilson-Ewing (UNB): So,
Edward Wilson-Ewing (UNB): Do you mean the enterprise or the horizon.
Johannes Münch: Outer
Edward Wilson-Ewing (UNB): Right. So this is just the usual outer horizon. That's essentially at the short short radius.
Edward Wilson-Ewing (UNB): Plus some very small quantum gravity affects that we can
Edward Wilson-Ewing (UNB): Neglect here.
Johannes Münch: So, so some little bit more about the fact because because if you just
Johannes Münch: Think about the exterior space time basically the horizon should be a causal horizon and once you met I came across this causal arising never can come back. Right.
Edward Wilson-Ewing (UNB): So if you remember for for
Edward Wilson-Ewing (UNB): For a test field. That's true.
Edward Wilson-Ewing (UNB): But if you have matter which is back reacting, then that's. And again, remember that the equations emotion here, not the equations emotional GR so the the intuition developed in GR just isn't
Edward Wilson-Ewing (UNB): Clickable stuff. So, it is true that if you have a causal horizon and you have a test particle, then it'll never come back up.
Edward Wilson-Ewing (UNB): But here we have a matter of field which is very much back reacting on the geometry.
Johannes Münch: Yeah. Yes. I'm not completely sure about this because there wasn't a paper on black hole collapsed by boy. Well done to other collaborators, I
Johannes Münch: Forgot fortunately in 2004 or six or something around this where they actually counted the same problem that they had a space site or they had matter which was bouncing
Johannes Münch: But they were not able to describe how the bounce proceeds. Once you reach the horizon again. So you're personalizing your bounce and then you reach it again. And then I was not sure how they were not sure how to proceed afterwards and
Edward Wilson-Ewing (UNB): Right. So I'd have to check that paper and detailed to to fully answer that. But here I mean we do know how to proceed, because we have these equations emotion here.
Edward Wilson-Ewing (UNB): So the, the only question is, we have to solve them, which of course is easier said than done. I mean, these are quite complicated. Especially if you have some sort of discontinuity.
Edward Wilson-Ewing (UNB): So in principle we know to do in practice. We're working on it.
Edward Wilson-Ewing (UNB): But the point here is that it's absolutely true that if you have a test particle once it passes the horizon. It's not coming back.
Edward Wilson-Ewing (UNB): But here you have a matter of field which is very much backtracking on the geometry.
Edward Wilson-Ewing (UNB): And furthermore, not according time science equations right these are modified
Johannes Münch: Yes, but but still you have the effective
Johannes Münch: FaceTime, which on the line. Yeah. Like, like the mathematics of differential geometry, so on.
Johannes Münch: And so I'm not sure if it's really a thing of the equation of more human. Rather, the notional causal writing things like this.
Abhay Vasant Ashtekar: So let me just rephrase what you on this is saying and see if this makes sense to you so you only see saying that, well, but I mean you if in fact you're saying that there is a giving horizon. So there's another vector field. And there's a killing horizon. Right.
Abhay Vasant Ashtekar: So it's, it's a standard sure to it.
Abhay Vasant Ashtekar: And then the the killing records tangential to the know service, then the statement, he's saying is that, then whatever is inside just by causally because you're gonna you're gonna metric here and the causal structure of that metric would be such that
Abhay Vasant Ashtekar: Whatever is sort of on the one side
Abhay Vasant Ashtekar: Could never get out
Edward Wilson-Ewing (UNB): Okay, I'm here. I think I should be careful when I speak of
Edward Wilson-Ewing (UNB): This powder horizon, hear me and apparent horizon.
Edward Wilson-Ewing (UNB): We don't have a killing vector because this is a dynamical space time
Abhay Vasant Ashtekar: Why is it that it's outside the matter it
Edward Wilson-Ewing (UNB): Well, the matter of strengths that say out here right amount of stress very far out collapses in and then eventually bounces back in
Abhay Vasant Ashtekar: I think people got interested in the picture that you have here, which is that, well, the matter is actually collapsed in
Abhay Vasant Ashtekar: And then
Abhay Vasant Ashtekar: Then is there that out the horizon is still there. If. What's the matter is actually
Abhay Vasant Ashtekar: collapsed in and if there is out of horizon there then just by cause of structure if it is a minus, plus, plus, plus signature metric. And there's a closet structure, then whatever is so to say inside
Abhay Vasant Ashtekar: It would mean, is this like an adequate right i mean what it is you cannot tell drivers that boundary. So that is this question. So I don't think it has to do with the equations of butchering, this is
Carlo Rovelli: It cannot pick
Edward Wilson-Ewing (UNB): Yeah, I mean, let me just say something, I'll let Carla jump in. After but here again I agree that if you have a test particle once it passes your outer horizon is not coming back. There's no question about that. It's when you have
Edward Wilson-Ewing (UNB): A minor field which is back reacting on the geometry and then your geometry can change.
Edward Wilson-Ewing (UNB): And then it will be able to to come back out.
Edward Wilson-Ewing (UNB): Sorry, Carla. You want to say something.
Carlo Rovelli: Yes, something along these lines. The, the, what you said is correct. I think what am I saying is that if you just look a little bit outside X outer just on an outside this if you assume that you are in in
Carlo Rovelli: In the classical fully in the classical
Carlo Rovelli: Approximation, then there's no way to to to
Carlo Rovelli: I mean the outside parties counseling closed. There's nothing that can come in. But I think the point is that your patients here my violate the classical artists and equations one
I don't even
Abhay Vasant Ashtekar: Know, no. But there's nothing to the eastern equation it is just different to john because he was saying.
Carlo Rovelli: No, no, but yeah. By then, then the then, the point is, what is not a spacetime on weekdays a dynamic because it's a dynamic space time itself. So it's a it's going to change according to
Abhay Vasant Ashtekar: Show. So it just the diagram is misleading. That's all.
Carlo Rovelli: Yeah yeah yeah
Abhay Vasant Ashtekar: He's a little bit
Carlo Rovelli: If one if one if one reads status as right as a council structure on which the star is expanding stories is moving, then it doesn't work, but that's
Carlo Rovelli: I think we shouldn't blow ready
Edward Wilson-Ewing (UNB): Here. Sorry. The late calls really meant just for test particles.
Abhay Vasant Ashtekar: So,
Edward Wilson-Ewing (UNB): This instance of time.
Abhay Vasant Ashtekar: Because the light goes, I'm not. They don't refer to it as particles like guns. I just like guns.
Abhay Vasant Ashtekar: Though I think the statement is basically that this is going to be
Abhay Vasant Ashtekar: Probably an isolated horizon for a little while because you know the matter is inside all the way that you're drawing here.
Abhay Vasant Ashtekar: But then the statement is a mattress coming out.
Abhay Vasant Ashtekar: And before
Edward Wilson-Ewing (UNB): I mean,
Abhay Vasant Ashtekar: Sorry.
Abhay Vasant Ashtekar: Yes. Like, like, like the white space time. Is it going to be in fact that the is going to be
Abhay Vasant Ashtekar: So you aren't as it's going to be now for a little while, but the statement is that the end matter is going to come out.
Abhay Vasant Ashtekar: Yeah, it comes out the matter comes out and then it becomes a
Abhay Vasant Ashtekar: Dynamical horizon, and that is why there is a good chance that scribe will be complete and salsa. So this picture up here is is this is not incorrect busy misleading in the sense that at this is our time, it is true that there is something now.
Edward Wilson-Ewing (UNB): If you prefer that this is
Edward Wilson-Ewing (UNB): What it looks like an instance of time.
Edward Wilson-Ewing (UNB): Exactly. And as time evolves. This will change.
Abhay Vasant Ashtekar: Exactly. And it changes qualitatively. What's the matter comes out when it becomes dynamic, is that okay yeah honest because if you're done, then where to go to the next question.
Johannes Münch: Yes, thank you. All right.
Abhay Vasant Ashtekar: I think Danny Lee has a question or comment. Yeah.
Daniele Pranzetti: Hi ahead, I'm sorry. I missed the first for me. So maybe you said this, but I just went on this and be better how you derive your effect of equations because
Daniele Pranzetti: I seen derivatives there. So it seems to me you're taking some parameters to zero or mean some discrete skills to zero or how can the relative
Edward Wilson-Ewing (UNB): Right, so here
Edward Wilson-Ewing (UNB): What I did is I just look at circle symmetry. So, of course, there's some x dependence right some real dependence.
Edward Wilson-Ewing (UNB): And I'm not looking only at the inside. I'm looking at the full space time with both the interior of the horizon and the exterior
Edward Wilson-Ewing (UNB): And after that I gauge fixed
Edward Wilson-Ewing (UNB): So, and by gage fixing here. I mean specifically setting this term here to be x squared.
Edward Wilson-Ewing (UNB): And then after that I include the whole on me corrections.
Edward Wilson-Ewing (UNB): I'm not sure if that answers your question.
Daniele Pranzetti: I mean, because usually every derivatives in the classical myth thing becomes a discrete
Abhay Vasant Ashtekar: Different. No, no, no.
Edward Wilson-Ewing (UNB): I'm remaining at the effect of level here so I haven't. So you're right. The next step that I would do, which we haven't done here. But what the next step would be to them to securitize and then define the quantum theory and lattice.
Daniele Pranzetti: Okay, so there's some direction, basically you're taking this continuous in some so this
Edward Wilson-Ewing (UNB): Is not one treating all of the directions is continuous.
Edward Wilson-Ewing (UNB): But anyway, yeah, at the quantum level, I would have to, you know, introduce a lattice.
Daniele Pranzetti: So yep only one squeaked in a parameter in this game, you're seeing or these are the only one delta, not like a date on this fear there is no delta, there is no grass.
Edward Wilson-Ewing (UNB): That's right, because of the gauge fixing that have done now.
Abhay Vasant Ashtekar: I think there's confusion at a
Abhay Vasant Ashtekar: Minus, minus three level, so to say. So these are the 50 questions a lot. Look, Congress biology, for example, right. So it's not that one is actually taking some
Abhay Vasant Ashtekar: One is not he is not doing like things that various people like are doing when they're coming from Luke condom guy with you to do Congress Margie by introducing some some some state there and some code and states and discreet state and then
Edward Wilson-Ewing (UNB): I read
Abhay Vasant Ashtekar: The market. So he's not doing that at all. So the statement is this is really proceeding as in look Congress mythology in which you first have just
Abhay Vasant Ashtekar: The medicine, this, this, this really super space right of the where everything just depends on our so it gets particular symmetric media super space and one just start from there. One doesn't try to come
Abhay Vasant Ashtekar: This quantization from a flow theory and therefore everything is continuous from the beginning, the effective date and an end date. Yeah.
Edward Wilson-Ewing (UNB): That's right. And of course, I mean an interesting open problem would be to see how to do that to start from the full theory and then come down.
Daniele Pranzetti: Okay, but also even from that point of view, you still recent like in your model by your true discrete as parameters. Right. Also on the sphere, even though you you down the road from the food theory.
Edward Wilson-Ewing (UNB): So it sounds to what you mean the to the screeners
Daniele Pranzetti: Me like there is the Epson Epson next if you want an extra associated to links on the sphere and act transistor radio links.
Abhay Vasant Ashtekar: That are links.
Daniele Pranzetti: Yeah, but I mean the justification for introducing the parameters.
Edward Wilson-Ewing (UNB): So, so here what happens is that because of the gauge fixing. I only have to take his enemies in the angular directions.
Daniele Pranzetti: Okay, so it's like taking the other option to zero best really kind of
Edward Wilson-Ewing (UNB): I'm not really because because of the gauge fixing the connection in the real direction is then rewritten in terms of the connection and the aerial directions are in the angular directions.
Edward Wilson-Ewing (UNB): So there's there's some mixing here.
Daniele Pranzetti: Okay, so you only have one parameter that determines that is quickness.
Edward Wilson-Ewing (UNB): That's right, basically. Yeah. And that's essentially what we set to
Edward Wilson-Ewing (UNB): That we set that physical length to be equal to the square where the recap.
Edward Wilson-Ewing (UNB): Okay, so. So again, I mean, this is very much following he LTC
Abhay Vasant Ashtekar: Is best. Not a thing. It doesn't this cretinous but just to think of there was constant calamitous nondescript this
Yeah yeah
Daniele Pranzetti: But so you have only one on one, two parameters.
Edward Wilson-Ewing (UNB): That's right, yeah.
Abhay Vasant Ashtekar: Okay Kong Zang has a question.
Cong Zhang: Yes, I just have a small question about
Cong Zhang: This minimal value of this x. So here, your explanation about this minimum value is data. So this minimal value is the end of the vacuum solution.
Cong Zhang: So my question is, it is possible that here you have this minimum value of x, just because that this x is not a GU to coordinate in your effective space time which cannot cover the whole space time
Edward Wilson-Ewing (UNB): I mean, that's certainly a possibility in general. And then this is what both Carlo and Johan us were suggesting earlier and
Edward Wilson-Ewing (UNB): At first, that something that's truly worth looking into. But from at least my point of view, the fact that when we add in matter we get rid of that issue completely to me suggests that this is more a question of trying to
Edward Wilson-Ewing (UNB): You know, treat has vacuum of space time where you really should have some matter content. So the fact that it goes away so nicely.
Edward Wilson-Ewing (UNB): When you add in a matter of field to me suggests that this is really just an artifact of, you know, looking only the vacuum case when you add in matter, then this, this goes away. But I agree that a priori, that could be a possibility. Absolutely.
Cong Zhang: OK. OK, I see. Thank you. Thank you, you
Johannes Münch: Have a comment on this.
Abhay Vasant Ashtekar: Guy.
Johannes Münch: And I think in the so I think it's not really a matter, matter of matter on me because
Johannes Münch: I think in the moment where you go to the young, the bounce and you have increasing x. Again, you essentially implicitly assume that your, your white hole in quotation marks branch is essentially the same one as the black hole branch.
You know, it's nothing.
Edward Wilson-Ewing (UNB): Because it's moving up much more slowly, it collapses in a timescale. That's essentially the mass
Edward Wilson-Ewing (UNB): And the expansion as is slower, right, sorry.
Johannes Münch: That's the metric timescale, I'm just talking about the solution outside the matter.
Carlo Rovelli: I think
Carlo Rovelli: The solution.
Edward Wilson-Ewing (UNB): The matter is stationary
Yes, but but
Johannes Münch: It's hard to explain. Okay.
Edward Wilson-Ewing (UNB): Go ahead.
Johannes Münch: So I think at the moment you you go beyond the minimum value because if you think about postcard diagrams, you essentially have to
Johannes Münch: So you can write down to the collapse of the classical black hole is drawing a shorter course Costco diagram and then draw the line of matter in this diagram right and
Johannes Münch: So, so your exterior space time is only valid up to this dynamic line of
Johannes Münch: The outermost shell of your columns. Right. And in the moment it hits the singularity, or in your case that the minimal value. That should be the the singularity. Yes, so that the
Johannes Münch: Time like surface which classically is the singularity, but it's now your, your minimal value this X Men. And then the question is how you proceed. And I think you just implicitly just mimic the same exterior space time
Johannes Münch: Can you follow roughly what I'm trying to say.
Edward Wilson-Ewing (UNB): Um, well, let me, let me try to tell me if my answer is not for my answer your question, but so what we have is that we have me. Can we just go back here.
Edward Wilson-Ewing (UNB): We have these equations emotion and we have
Edward Wilson-Ewing (UNB): Our hardest field and we can just solve these equations emotion. Right. So, what, what I do is I say, I'll give you some initial conditions.
Edward Wilson-Ewing (UNB): Right, have a star that has some radius. And that's vacuum outside. So these are my initial conditions and then I just let the system evolve using these equations emotion.
Edward Wilson-Ewing (UNB): And what happens is that the star will contract.
Edward Wilson-Ewing (UNB): It will reach some minimum value and then we'll bounce and it'll come back out again.
Edward Wilson-Ewing (UNB): Now the equations emotion are easy to solve for the contract in part because the edge effects are negligible and you can throw them away.
Edward Wilson-Ewing (UNB): For the expanding case, it's much harder solve. And so we're working on that right now.
Edward Wilson-Ewing (UNB): But this is very much just a question of right we have some equations, emotional, we can solve them. And then from once we've solved equations emotion, then we can reconstruct the space time
Yes. Okay.
Johannes Münch: So, so if you think about it, but
Johannes Münch: I'm not sure if it's really to to summarize my comment I'm not really sure if you can avoid this. The second branch of all these white, black and white for solutions by just adding metal finishing my calling. But I have to study your, your, your work in more detail to understand
Edward Wilson-Ewing (UNB): Thank you. No problem. If there's something that you know you think is worth discussing, please let me know.
Abhay Vasant Ashtekar: Okay, just go.
Francesca Vidotto: I have a question regarding the expanding face so you know that this is an ongoing work. So probably you don't have it yet an answer, but I just wanted to put something on the table to think about maybe for the future.
Francesca Vidotto: So when thinking about expanding face. We had a lot of discussions with the people in Murray, the like he's been in general versa longer I and so on. And he brought his word about the fact that
Francesca Vidotto: It's very important to know what is the speed of the expansion and it will be preferable to have a very quick especial rather than this low one because we, the
Francesca Vidotto: For this function is not fast enough, then there is the problem of a possible recall apps. So any stability of the day. Wait, old face.
Francesca Vidotto: On your face, whatever you want to call it. So I always think about this expanding face as being a dynamic of processing which have also the mantle be taken into account.
Francesca Vidotto: So these changes a lot to the the picture. So usually when all these instability arguments are discussing that nobody's discussing the fact that that, in fact, if you have an expansion. There is a lot of math of that coming out.
Francesca Vidotto: From the riser. So yeah, maybe two things to think about. One is the speed in general and they're all of matter. Yeah.
Edward Wilson-Ewing (UNB): I agree with both of those points. Um, and, but let me just add to that, there are usually there are two differences, I think.
Edward Wilson-Ewing (UNB): In in what we're doing and the usual calculations for these white hole instabilities
Edward Wilson-Ewing (UNB): The first one is you say is that matter. Right. That's a big difference. And the second one is that usually when they talk about this white hole instability. It's a true white holes FaceTime
Edward Wilson-Ewing (UNB): And here, that's not exactly what we have right we have, you know, some region which which is trapped at least for some period of time and then another region which is anti trap. So there are some differences.
Edward Wilson-Ewing (UNB): And how these all combine. I'm not sure yet. But yes, this is certainly something that we're looking at.
Abhay Vasant Ashtekar: Okay, so God Moses, the Lord is had anybody else has any questions or comments.
Abhay Vasant Ashtekar: Yeah. JOHN Jonathan
Jonathan Engle: Yes, so maybe this is a very simple question. Um, since you have a model of
Jonathan Engle: Oh, I see. I think I've answered my own question. I was wondering why
Jonathan Engle: Don't see any Hawking radiation.
Jonathan Engle: So, the better. But I guess the point is that you're just using effective equation. So you're really treating the matter quantum mechanically, but I mean it would be interesting. One could also see Hawking radiation in a model like this, but that's
Edward Wilson-Ewing (UNB): Probably not. Yeah, I would love to do that.
Jonathan Engle: Yes, yeah.
Edward Wilson-Ewing (UNB): I don't have to
Jonathan Engle: Talk.
Edward Wilson-Ewing (UNB): Thank you so
Good.
Abhay Vasant Ashtekar: Good Jonathan, you're done. Right.
Jonathan Engle: Yeah. Yes.
Abhay Vasant Ashtekar: Okay, you can move the hand.
Abhay Vasant Ashtekar: Yes.
Very quick
Abhay Vasant Ashtekar: Okay punches.
Francesca Vidotto: And follow up with that in order to study.
Francesca Vidotto: Okay, you may want to check the work of
Francesca Vidotto: Get into. So look at this, the treatment is a classical one. So it should be applicable to what you are doing.
Edward Wilson-Ewing (UNB): Okay, I'll take a look at that. Thank you.
Abhay Vasant Ashtekar: But I mean that is basically patching white space times. So I think you could pass the space time to she wanted but
Abhay Vasant Ashtekar: could not do scale of field. Is it just completely difficult in sort of classical scale of field is sort of the scale of field collapses for the
Abhay Vasant Ashtekar: Does collapse.
Edward Wilson-Ewing (UNB): Right. So that's something I'm thinking about, um, I, I don't have an answer yet because I haven't gotten very far with this, but this is definitely something that's on my plate.
Abhay Vasant Ashtekar: Because that would then also, you know, in some sense, the natural part to the Hawking.
Abhay Vasant Ashtekar: Radius. Right. Absolutely.
Abhay Vasant Ashtekar: And also, anyway. I mean, that's the fundamental level, we shouldn't be talking about so that
Abhay Vasant Ashtekar: And just to sort of summarize. I mean, you know, of course, you arrived at this particular
Abhay Vasant Ashtekar: Calculations falling seven steps in some ways I mean you want you to do the first the vacuum case. And then you realize that somehow there is a issue. And then that issue sort of naturally led you to look at the
Abhay Vasant Ashtekar: The collapsing situation. But of course, logically, you could just forget about the first part altogether.
Abhay Vasant Ashtekar: Absolutely, absolutely. Logically, you can just say that, well, I mean, you know, it's important is much more realistic to talk about all these things.
Abhay Vasant Ashtekar: Not about studying black hole, but really the collapsing black hole because I know that Hawking radiation etc refers to collapse. And so what could actually just look at the collapsing backhaul and then see see what happens.
Edward Wilson-Ewing (UNB): Absolutely.
Abhay Vasant Ashtekar: The baby. And then from that perspective, then what will happen if we had looked at this white space times like this Martinez.
Abhay Vasant Ashtekar: Is looking at
Edward Wilson-Ewing (UNB): Well, I'm
Edward Wilson-Ewing (UNB): Vida is dust is it
Abhay Vasant Ashtekar: No, it's not like it's not it's not a strict
Edward Wilson-Ewing (UNB): Um, I think you need a different action.
Edward Wilson-Ewing (UNB): Because this dust is necessarily time. Like I said, I'm so I would expect that you could do it.
Abhay Vasant Ashtekar: But yeah, because if I
Edward Wilson-Ewing (UNB): Had to go back a few steps and the data.
Abhay Vasant Ashtekar: Just started Einstein's equation, right. We don't have to go back to the action. This
Abhay Vasant Ashtekar: Because, you know, after all, your okay
Edward Wilson-Ewing (UNB): Well, the thing is, let me just mention here.
Edward Wilson-Ewing (UNB): Here we're really using the desktop gauge
Edward Wilson-Ewing (UNB): So we're using the dust as o'clock I that I imagined wouldn't be possible or for an oldest right so i think that you could probably adapt it, but I'm not sure. I mean, I would require a little bit of work.
Abhay Vasant Ashtekar: That will just make
Abhay Vasant Ashtekar: Connections with what Francesco said, Yeah.
Abhay Vasant Ashtekar: Okay, so I don't see any further.
Carlo Rovelli: By. Can I make a note is a known physics.
Carlo Rovelli: Point system.
Carlo Rovelli: In this this meeting emerged from from the older telephone one. So, so we're used to not look at one another, but I would like to
Carlo Rovelli: Bind that video that zoom doesn't is not overcharged everybody keeps the video on and it's much more pleasant to give a talk. If you see the faces of people, so I
Carlo Rovelli: I would invite me, of course. Everybody's free, but I would invite people to show up their faces. It's nice to see France, of course, be unmuted. But with video on
Abhay Vasant Ashtekar: It just a lot of times, you know, the internet connection is unstable and if the video is on the question more data bank and so a lot of people like me. We keep it off, just because of the
Abhay Vasant Ashtekar: Instability good mix.
Carlo Rovelli: Right, right, if you have, if you have a connection problem, of course, I understand, and people may have reasons but it's, I just, you know, it's nice to see faces for those who have good connections, but
Abhay Vasant Ashtekar: Okay, so thank you very much again and and I guess this is the
Abhay Vasant Ashtekar: I mean, I guess we'll, we'll get get back in touch Horry and others will get back in touch, about the next meeting and topics so
Abhay Vasant Ashtekar: Thank you everyone for all your questions and comments I
Edward Wilson-Ewing (UNB): Was very, it was very enjoyable to to give this talk. So thank you.