Jorge Pullin: Okay, so today we have two speakers Fabio melee and your hand is Munch who speak about direct observers and BB type variables for effective polymer black holes.
Regensburg: Thank you. Hello. He's speaking
Regensburg: First of all, I would like to thank
Regensburg: In the name of both of us for the opportunity to give this talk here and present our latest work in the seminar. We published two papers today and yesterday.
Regensburg: Where this talk is based on so you can find them on archive under these numbers and they just work with it together with no my own offering at the University of Liverpool.
And
Regensburg: Let me start by giving you a quick motivation. Why we study black holes and probably don't need to tell you that black holes are of great interest in basically all main quantum gravity approaches as essentially they are or
Regensburg: As basically they they allow or they have the connection between quantum physics and gravitation physics and already at the horizon. We have phenomena phenomena like the hockey radiation informational products, but also
Regensburg: Black hole has a singularity, which is of course of great interest in quantum gravity.
Regensburg: Also, there is a quite pragmatic reason to to study black holes and that is that
Regensburg: We're working on the sponsored set up so we are certainly symmetric and static, which is quite simple strictly soon. Sure, reduce setting. And here we can actually do computations. And this might also provide us with better understanding about full loop on right
Regensburg: Furthermore, for the group Ian links book this this is of interest because we did some some novel and collaborators and also asked, we did some work on
Regensburg: The Singularity resolution of in the context of there we studied cosmological similarities and we'd like to extend this work, which we have done here asked to set up of black holes.
Regensburg: And for that reason, we started to to study effective models of black holes and so classical geometries, which are quantum corrected and where the quantum corrections are inspired by Luke quantum gravity and
Regensburg: Yeah, you can see that it was that there was a lot of previous f4 in the field, how black or should look like about what a black hole is in new quantum gravity.
Regensburg: But although or yeah as a so much work. They still not really consensus about how black or should actually look like gravity. So, there is still something
Regensburg: Where work is done. And essentially, we, we think that that can use techniques from from Groupon gravity to
Regensburg: To tackle the blog or the problem of black holes because if you study the interior of a black hole in a little bit more detail you
Regensburg: And you notice that it's actually a contrast exact cosmological structure. So you get the idea to just use techniques from the quantum cosmology. She's polymerization and
Regensburg: Use that in this generalized cosmological setting and then you have a theory of black hole, but of course it's not that simple. As I just said.
Regensburg: There are many subtleties as the occurrence of do of those which I will talk about and also they are different schemes and different schemes of these different schemes has different departments, different about this advantages and we also present a new scheme in this talk.
Regensburg: The talk is structured as follows is essentially there are two parts. I will do the first part.
Regensburg: Is about Dr observers and our first present the classical theory and then I will continue.
Regensburg: With the effective quantum theory, the role of direct, direct comm zones there in and they will also studied PREVIOUS MODELS AND DR results there.
Regensburg: The second part is about the new variables we introduced that is there is for Fabio will talk about and they explains how we get these adopted variables for this effect palm and black hole and then he will
Regensburg: Explain how we overcome previous limitations for the physical viability, the we finish the talk, then by giving a conclusion and outlook.
Regensburg: Then let me start with part one, the mass and horizon Dr zones in Palma block black hole models.
Regensburg: And so let me first tell you some things about classic is setting to make you familiar with our notation.
Regensburg: And so we're in the circus metric and static setting in. For this you can do this answers for the metric and indeed you observed during the interior of a black hole.
Regensburg: And then this a bar in this n might actually negative. So the time sort of take on it here becomes space, like in the article on it.
Regensburg: Becomes time like and then this is indeed homogeneous, but honestly tropic but it's a kind of a cosmological space time and has is a so called capacities X cosmology.
Regensburg: For doing then the whole cannot canonical analysis and so on.
Regensburg: We have to regularize then this non contact T direction here to make the integrates all finite for that we introduce
Regensburg: The same spirit as also done previous models in congress module we introduce a fuel cell of
Regensburg: Go on and size or not. And we also introduced this curly or not, which essentially just integral over this metric component, a year over the future cell and we evaluate this.
Regensburg: At a certain reference point and we will need this later on because that is actually on an independent, but of course it depends on this traditional reference point people chose here.
Regensburg: And as canonical variables. We then use essentially this A, which is the integrated version of this a bar which piece of the metric over the future cell.
Regensburg: And also appearing also the small end which is the product of this interview and this this a year that will appear later computations and turns out that this small and is actually launch multiply then generating the hammer 20 constraint.
Regensburg: And
Regensburg: Probably for for f g people, it's more familiar to to translate this into connection variables there was work which has worked out how to
Regensburg: How this has to look like in connection there. And so then you can write down this line element, you see that for the interior where this in this inner negative, we can map this metric, of course, so we can match these two metrics. If we identify the capital T on and the are here.
Regensburg: The x coordinate here with the team here and the canonical variables are related, like this. So this metric description. This is actually exactly the equivalent for the interior of the black hole.
Regensburg: You can then go on into the whole economic analysis right down the hammer 20 and derive the Queen's motion. And if you solve the equations of motion, you get essentially this solutions. The exact form of the solutions are not important here. But what you observe here is that essentially
Regensburg: So they are three integration concepts, but this is what a here, we can just interpret that as a shift in the time coordinate and so we can set this to to one without loss of generality, and then we just left with two integration Constance which is this see not here in this PC not here.
Regensburg: And
Regensburg: To really find the final
Regensburg: Or we should somehow fix these integration constants. Now, and for that we can reconstruct the line element for that we take this a here reconstruct this OUT OF THE PB in the PC and we express that in term of B, which is the aerial radius of our metric
Regensburg: And doing that gives us some. So the advantage of that is essentially expressing stuff in terms of expressing quantities in terms of the speed
Regensburg: Is quality independent because this be appeases scholar in this factory symmetric setting.
Regensburg: Where I then in this a of the year. And from then we can already read off that it actually looks like.
Regensburg: looks similar to to the shield solution when we interpret this spirit of PC PC, not as the size of the market horizon, but we still have this these constants. He in front, which would like to get rid
Regensburg: And actually we can really get rid of that by just doing a quantum transformation. So
Regensburg: We define this new time call on it and Marie scale this expo on it and then we end up with exactly this line element and
Regensburg: What do you see is that this is really as expected. That is just a Russian metric for the interior of the black hole.
Regensburg: And what but what he furthermore observe is that only this our horizon. So this spirit of PC not peace in this final metric. So the value of seen
Regensburg: As normal no role for this line element here.
Regensburg: So we can try to understand this. Now, the better. So
Regensburg: If you count the canonical degrees of freedom, we find that our face space has essentially four degrees of freedom, but we also have a first class constraint which gives us two degrees of freedoms, we should end up with two physical degrees of freedom.
Regensburg: And hence, we should have to direct observers to fix their initial values, and indeed the free free look for themselves, you find that this one for this for the sponsor horizon, which we can write as this on show that we use just to this value our horizon. Same as the spread of this
Regensburg: Of this PC not we can also find another demo, which is, for example, see times PC that is also that also commutes with a hematoma constraint and unsure, there's just the product of these initial values.
Regensburg: And impressive. You can find awesome different Dr absorbs for us some some freedom, which was the second one.
Regensburg: But that doesn't change the analysis here and what we observe is that only this our reason is
Regensburg: Is physically. So once we fixed the value of this year was over the horizon, we saw in the previous slides here. And then our metric is fully determined and everything's
Regensburg: Everything's fixed wireless completely independent what we do with this d. So we could give this different values, but the physical metric won't be affected by this. So,
Regensburg: This place. Actually, no, no physical road. And we see this, we see this by two facts. The one is that it just does not appear in the metrics. So it cannot have any physical relevance, but we also see that
Regensburg: If you study how this see in this PC scale with the future structure, you see that this product just gaze linear with risk is this
Regensburg: Solution length. So this value of these actually dependent on which reduce yourself chose. So also, that tells us this d cannot really be physical quantity as depends on this financial structure.
Regensburg: And we can explain
Regensburg: This some of this mismatch of having to dr ASOS which are by definition gauge independent
Regensburg: But only one of them being actually relevant in physical metric or we can actually get rid of one of them by just doing a quantum transformation. So, so, Gage transformation and we can explain this by but residual different ones and
Regensburg: What we observe is that we want to get rid of this this D. We did this quantum transformation. So we just reschedule the exponent by by a constant. And when we see that this a Bob, which is the quantity appearing in in the metric I introduced on the first slide, slide.
Regensburg: That this actually picks up just the same factor here just inverse
Regensburg: Sorts of we see that this a bar is sensitive to that quantum transformation. But if we study the, the quantity which appears in our Hamiltonian which is this is a year. So this integrated
Regensburg: So, so the integrated a bar or the future cell, we see that if you change the components that then the financial cell becomes rescheduled but also miss a becomes very scared.
Regensburg: And they become reschedule exactly in a way that the product is the same. So the trends. So the corner transformation.
Regensburg: Which risk is just x coordinate is the identity on the face space. So this transformations simply not present in the face space. So our canonical gear and those can also not know about this transformation. So
Regensburg: They there's no generator for for any
Regensburg: For any transformation of this kind, as it is on the face face good entity. So yourselves cannot be
Regensburg: Cannot see that they are independent. With regard of this remaining injury free, but what we see is that the physical metric is actually affected. This is what we see here so we can actually get rid of additional degrees of freedom here.
Regensburg: And
Regensburg: We can furthermore conclude that in or we can see that in a different way that essentially introduced this producer cell and just the introduction of this beautiful cell.
Regensburg: Gave us these residual different war films or gave us so just integrating here the quantities over the future self, and that led
Regensburg: Led to this residual the few more films being the identity on the face face.
Regensburg: And that means these residual different offices are actually not present on the face face, but we can still see that quantities are sensitive to these
Regensburg: These transformations through the video should sell depends. So this am the slides before was dependent
Regensburg: Linearly dependent on this or not. And that reflects that. It's actually a quantity which was integrated over the fuel cell enhances
Regensburg: Sensitive to this residual different offices.
Florida Atlantic University: Ask a question or make a remark.
Florida Atlantic University: So if you. I think that because you're thinking about these residual different morph isms passively in terms of changes of coordinates and
Florida Atlantic University: And you're rescaling the cell at the same time. That's what's making it the identity on the face space. But for example, if you were to fix.
Florida Atlantic University: You know, the, the cell is really a background structure and you could if you leave that fixed
Florida Atlantic University: And you only do the coordinate transformation, you will see an effect on the face and and of course there's there's an active version of this transformation, which is of course an actual defeat Morpheus. And if you think of
Florida Atlantic University: Think of it in terms of that you will see that the the action on the face space is non trivial. It's just not canonical. So it's just a remark. I don't know if you want to respond to that.
Regensburg: Yes. Yeah, yeah. That is partially true in the sense that this or not is actually the size of the future sell in the tea or in, you know, in the teacher.
Regensburg: Know, in the next chart. So, and not is the size of the future selling this x chart. So if we keep these are not finite
Regensburg: If these are not constantly the next chart is will change in the white chart. So the solution, the physical size of solution cell does not change in in this
Regensburg: Consideration here. But you're right. You can also ask like just risque. The fuchsia fuchsia cell just making double as lush or something.
Regensburg: Then they will be non trivial on the face base, so that will map. This is a to twice a and but this is also know the canonical transformation is to just said.
Florida Atlantic University: Or you can think of it the other way you could keep the cell fixed and do a coordinate transformation is usually
Florida Atlantic University: I mean the the passive version of different more physicians is usually considered to be coordinate transformations and there's no real reason to scale the cell at the same time.
Florida Atlantic University: And that way you'll also get a non trivial action on the face, but will be non canonical
Regensburg: Yes, but actually here, we do not scale the cell
Regensburg: And so this L not is the size of solution selling X coordinate
Regensburg: So, and then we keep the, the size of the future sell in x coordinate fixed. So that's why we introduce here, this quantity
Regensburg: So there's currently and not that remains the same. If we change the coordinates and why the, the value of this this or not you, that will change in the different continents, but this this year will be the same. So, we do not really scale.
Regensburg: The physical size of the future set, but of course the appearance or the future sell in different on changes.
Regensburg: Yeah, okay. I mean, it's a little bit satellite to agree.
Regensburg: Yeah, we can maybe discuss a little bit more
Okay.
Regensburg: Yes. So, so this transformation was was not present on the face space or we can still see that qualities are
Regensburg: Sensitive to this residual different more business by having a not dependency in they're
Regensburg: Having they're not dependent. So if you're really scared if you do sell by by a factor to, for example, this a but also this idea of observe D. We just reschedule by a factor of two.
Regensburg: But once we go back to the metric, the metrics actually sensitive to that transformation and this we can use to get rid of this Dr. D, but by use of these cometary escape.
Regensburg: So the conclusion here is that they're actually to dr observance on the classical face space, but only one of them is
Regensburg: Physically relevant and we got rid of one of them by just rescaling our continents and that absorbs one Dirac observable and the fiscal year direct observe, we can identify as essentially being the
Regensburg: The trousers horizon, which is in the classical setting the same. It's just twice the black hole mass and with this comes now morning
Regensburg: Because what you could think of is to construct a polymer quantum theory or effective theory of the black hole.
Regensburg: And then evaluate your solution somewhere in the classical regime and fix your integration constant of the of the quantum theory by means of the integration constantly fixed in the classical theory.
Regensburg: But as we have seen in the classical theory, there's ambiguity in fixing the integration constant as is this one year of those actually
Regensburg: completely arbitrary. So if you just mesh. These to some classical regime you map this arbitrariness of the quantity of the classical theory into the quantum theory. So
Regensburg: You have to be really careful here in the cases that the same year observed in the quantum theories actually physically relevant and that is exactly what we see in
Regensburg: Or what we saw on our previous paper and and also in previous work and I just want to these examples, I want to show you next slides slides.
Regensburg: So in February this year will be published a model for
Regensburg: The former model of black holes were introduced this VP variables and they have this relation. So this v two, v one P two P one
Regensburg: And they have this relation to the variables in conference to the connection variables and we
Regensburg: So you cannot do the cannot can do. Now, this cannot transformation derive the Hamiltonian and so on. And then we went to the effective former theory by just Palmer's a polarizing these moments happy by just mapping them into the sign. And we kept the customization scales we kept constant
Regensburg: And
Regensburg: Me this theory, we ended up with is exactly is actually analytical solvable. And what we get them for for the speed and the a
Regensburg: Exactly. These rather complicated expressions for sure. Again, not not relevant for the following. But what do you observe. He is, again, as expected, we have
Regensburg: To face base non true faith based degrees of freedom which which reflects that we have to integration consistency in the sea period here here.
Regensburg: And but what we see here is now that are coordinate appears in this non trivial square root or this combination of the square root combination. So if we just
Regensburg: reschedule the arco on and we cannot absorb the CEO, the D also not not a global factor will get rid of just multiplying by global factor is a will not help us to get rid of this seeing here. So we see that in this metric, they're
Regensburg: Actually both integration constancy up and we cannot just escape the actual owners to get rid of one say the d
Regensburg: And as they are both
Regensburg: Now, as they both appeared in physical metric, they should have both physical meaning, and indeed we can target them, and for that.
LSU Rel: Sorry. Can I ask a question on the previous slide.
Regensburg: Yes, of course. So
LSU Rel: I'm just confused with
LSU Rel: The various variables here. So, like, what is the physical interpretation of be in in your model like I know like you call them be. And we variables, but I'm just confused, whether they have the same interpretation as in Luke quantum cosmology.
Regensburg: Yeah, the interpretation is a little bit subtle and not completely relevant here but this v2. For example, measures somehow the the
Regensburg: Is like the arrow radius cute.
Regensburg: I know the the one is actually be airing radius. Q. This feature is related to to the A appearing the metric and maybe the
Regensburg: Yeah.
Regensburg: Um, this is Norbert let me make clarifying comment. So you may be misunderstanding the VB variables and the title with this slide here. So the beyond this slide. This is a standard
Regensburg: And B, which is conjugated to PB and standard connection variables. The VB variables that we find whichever kind of
Regensburg: Conceptual relation to the DB variables of upon cosmology will be discussing the next part of the talk by value. So this d here is the standard D from spiky symmetric connection variables.
LSU Rel: Okay, so be is just a canonical conjugate to PB
LSU Rel: Exactly. And so what is a physical interpretation of p one
Regensburg: P 200 said that is actually not relevant for this slide. I mean, you can read it all from the equations if you want but
LSU Rel: Maybe it is not relevant in your discussion, but I'm just confused that piece entering P one is entering in C and then P one is being poly memorized, rather than seeing polymerization. So I think it is probably going to be relevant later on.
LSU Rel: Julian Luke quantum cosmology, when we write see and
LSU Rel: When we when we have this face face of PB and B and PC and see the standard way or the heuristic were to obtain the effective dynamics is to polymerase connection and BS. On the other hand, you are a polarizing only part of see so
Regensburg: Yes, so the so the original goal of this work with this verbiage that you see here, which was not completely achieved in those variables was to memorize something
Regensburg: That makes physical sense to memorize the new not scheme, meaning that you would like to polymerase, something that is on shell related to a curvature skater that you would expect the large
LSU Rel: Ones quantum effects. Exactly. That's, that's the point I was coming to so
LSU Rel: It seems to me that so that you have chosen
LSU Rel: You have chosen to polymer eyes only that part of see which directly leads you to the bounds on freshmen scale and so on.
Regensburg: Yes. So what do you what what can probably say here is that these are almost curvature skaters. Okay.
LSU Rel: So if I if just to summarize, the only that part of CS being poly memorized, which immediately leads to the pole or a bound on freshman scholar.
Regensburg: But this is not quite true. And this slide, but it will be true in the next part of the talk.
LSU Rel: But that's, I think, like, we have to remember this, right, like in various models as since you were mentioning that there are various problems and all the models and so forth.
LSU Rel: We have to keep this in mind that none of the models previously kept in probably one paper of Leonardo Modesto
LSU Rel: People didn't make such a choice. People were working with a striker Barbara connection in their symmetry reduced
LSU Rel: Version and then only working with the polymerization of the connections C or B. We were not making particular choices.
LSU Rel: Of what part of the connection should be polymerase such that we are getting a bound on Cashman scale because then one is going away from the approach of loop quantum gravity, we are trying to polymerase something without any motivation coming from the quantum gravity.
Regensburg: Yes. I mean I have to agree with that statement. So the aim of this work was to try to construct a model that is physically viable.
Regensburg: And that's when
LSU Rel: You agree right like we agree that this model is not on not philosophy based as coming from the quantum gravity in the sense of the polymerization is not done of the connection and
Regensburg: It is not philosophically based on a model of gravity that good itself be built on Africa variables, if you would do.
LSU Rel: With that, I agree with that.
Regensburg: If you would look on gravity with variables that are similar to those, then it would be the same analog s
LSU Rel: Yeah, but we have to we have to then go back and derive everything from scratch like that right now we are
LSU Rel: Using a staggered Barbara variables to come to a classical face base then doing a symmetry reduction then choosing a part of that connection.
LSU Rel: To polymerase. So I that can be one model but i i well i think like we agree right now. Like we we are doing a construction in a very particular fashion, a very peculiar construction is happening here.
Regensburg: Yes, I completely agree. I mean, the idea of this construction again to say it was fine burbles that would lead to physically sensible dynamics were physically sensible means that quantum effects should be present. Once curvature skaters arch.
Jorge Pullin: Sure we continue
Jorge Pullin: Yeah.
Regensburg: Okay.
Regensburg: Okay, so we have seen that we cannot
Regensburg: Do I cannot coordinate transformation to get rid of one, A, B, C or D integration Constance here that means we we have to interpret what do they actually mean. And for that, we can write down
Regensburg: The following on can write down to the rack of servers which is FQ in this extra bar. I did not stay there face based pendants now explicitly here, but also they reduce this these combinations of CND
Regensburg: And we see that both of them has have physical meaning and we can interpret them by
Regensburg: Studying the US and talking regions in our space time and our space time looks some panels diagram is this one. So it's an infinite power of this single person black hole.
Regensburg: It looks similar to trash the black hole is one diagram and then you glue in. Finally, many on top of each other.
Regensburg: And then we study the as product regions and taking the limit for are going to classify it means we we are some way here in
Regensburg: in region one year and then we find that this region one is actually described by exactly this metric, which looks like, which is actually the fashion metric with sweatshirts, with the black hole mouse.
Regensburg: Or twice a black hole mouse being FQ can do the same thing for are going to minus infinity that means we go here through the, through the interior of the black and the white hole.
Regensburg: And then we end up in region, region three here. And again, then we find exactly the same line, line element.
Regensburg: Justice FQ bar here. So we interpret this FQ bias just twice the mass of the whiteboard. And so these two have both physical relevant interpretation here.
Regensburg: And you can also change the view points here. So you could could construct combinations of a black hole in Whitehall, which is quite complicated. And for example, you could evaluate the Cashman scholar.
Regensburg: At some given error radius some initial airy radius somewhere in region one and fix this fix the value here.
Regensburg: Which is essentially up to quantum corrections would then fix the value of the black hole mass, but what you can also do is to fix.
Regensburg: The value of, let's say, in principle, any other kosher scale. And then let's say we take either Richie scale and also fix the value of the literacy scale at some initial value be here.
Regensburg: And there is possible in the quantum theory because the Richie scale is zero plus or of quantum corrections. So, or in this case, number one. Number two.
Regensburg: So we can fix the value of these quantum corrections somewhere here in region one principle and then specifying these two values fix you uniquely the balance of the two masters have here.
Jorge Pullin: Can I ask for clarification. These are presumably ADM masters. Right.
Jorge Pullin: So you're evaluating. Did I not
Jorge Pullin: Yet one isn't on the I, not to the right and the other one. They are not left that area.
Regensburg: So this black hole is evaluate it and I not here and here. So vision wanted to describe the same describe both the black hole region where in Whitehall is the ATM acid I not here in here soon. Some reason three and four. Okay, thanks.
Regensburg: And we also study. Now these are observers also current in previous models.
Regensburg: And that is content of the paper, which today on archive and
Regensburg: For that we studied for simplicity reasons.
Regensburg: Not schemes and generalize me not schemes as their analytical analytical solutions available in principle what I'm going to tell here is valid for
Regensburg: Basically all morning speech have essentially these equations of motions that is true for the latest article made using paper, but also fully coolly Richie Singh paper and also other papers and similar
Regensburg: similar equations are written down by Modesto, which are slightly different concerning the permutation scale.
Regensburg: Optimization scales here. But in principle of equations motion have the same functional structure. And so you can again. So these equations of motion and you find that there again to integration constant you can target them.
Regensburg: Or combinations of these integrations essentially as the size. So the area radius of the black hole and the white hole.
Regensburg: Radius and we can construct your observers, which have these complicated for me again the
Regensburg: explicit expression is not relevant here, but just to show you, you can construct these and these are on shell. They are they are constantly on shell.
Regensburg: commute with the Hamiltonian and then fixing these values fixes you the size of the black hole and the vital radius.
Regensburg: And for for the papers of mood. So there was also an exterior space time available would with worse on top of that. Also as toxic stressors. So they also we can construct absorbs for the ATM mass on the corresponding sides.
Regensburg: Just to say this for completeness. But once you once you found this you actually notice that there are now.
Regensburg: Two degrees of freedom. So one is the size of the black hole radius. One is the size of the vital radius. That means that gives you an additional degree of freedom, which was not observed in these previous papers here some prints for you. You could now.
Regensburg: Go and revisit the arguments. So the plaque had arguments which were or whatever arguments done in these quantum theories
Regensburg: You can revisit them and can try to
Regensburg: Try to check if you now get new possibilities, because you have essentially one degree of freedom, more
Regensburg: To choose here.
Regensburg: And we can generalize this statement so we
Regensburg: Came to the following conclusion that basically whenever you have a problem model where one of the permutations scales is beautiful. Sally pendant. That was the case for the models I presented you so far.
Regensburg: And that is equivalent with having to physically Dirac absorbs and the explanation for that is essentially
Regensburg: In the classical theory, we have seen that one of the direct themselves was funded facility pennant but now we have have a polarization scale, which is also future Celtic can can just multiply this direct observable with with the super power of this
Regensburg: Of this permutation scale in the product then will not be
Regensburg: Finished and Sally pennant and that is actually then what appears in the final metric and but
Sorry.
PI: Every flight, what can you do
Regensburg: Not
Good.
Regensburg: Can you please repeat the question.
PI: On your show the black hole and wife always radio. Radio chemical be yo
Regensburg: Yes.
Regensburg: Yes. So there are several concerts appearing here. So there's this be not here. So the small be not here.
Regensburg: Which is something like square root of one plus data be square times gamma square with GM as the imagery parameter and this be not here is
Regensburg: I don't have the explicit
Regensburg: Expression here, but it's some function of this small be not here. So, but, but it does, but it is a constant for for delta
Regensburg: Against it depends on the music.
PI: Only or for me only
Regensburg: Has asked to be included.
Regensburg: Yes okay to
Regensburg: To get more confident. This is equivalence here. We also studied another class of
Regensburg: Another class of models were basically have variables for the presentation skills and both future sell independent and inconsistent so consistent with the statement here, we found that there's only one direct zone available.
Regensburg: So again, one is completely irrelevant does not appear in the final metric. And we showed that for him for a whole class of simple models where we're both future we're both permutations case of future sell independent
Regensburg: And then basically you issue to the following two boxes. So whenever you whenever you construct a polymer model of black holes, you're basically two options. Either you
Regensburg: Have variables where one of the permutation skills are future self dependent. And in that case, according to this observation here, you would have
Regensburg: To physically direct observers, which would correspond to the to mass or depending on the model. Maybe the two horizons and impress them. They are both unrelated. And so we can preserve choose a
Regensburg: Free will, and that gives you additional degree of or additional freedom in actually imposing whatever quantum condition you would like to satisfy and
Regensburg: Previous models was like in the model we presented presented earlier, there was the quantum condition was something like we would like to have a unique apiculture bound
Regensburg: And that restricted a relation between these two integration concepts between these initial conditions that the white from us actually a certain functional the black hole has the same
Regensburg: Happens or is expected to happen if you if you
Regensburg: Do other quantum conditions. So like black hat arguments are in the mood. So papers he also did arguments coming from full upon gravity and they also essentially
Regensburg: Indirectly fixed the relationship between the white or black or mass. So you're restricted the initial conditions to meet the quantum condition post. So the question we
Regensburg: Was rising then for us was like, can we circumvent this. So can we
Regensburg: Can we find actually variables or can we find a scheme in which we satisfy our chronic conditions which are chronic condition which is unique appa Kirshenbaum
Regensburg: But without fixing a relation between the initial conditions and that is the variables, which is far, we're going to talk about in a minute.
Regensburg: The other possibility is when you construct a problem, a model of Lycos that you best choose variables were both
Regensburg: presentation skills are financial sell independent and according to our observation that would lead them to just having one
Regensburg: Director of zone and this one direct comes over essentially a codes and both masters.
Regensburg: And so that is exactly what we found here so we can evaluate this directly or we can evaluate the metrics somewhere in on the black hole side and then can find what is the
Regensburg: What is the black mass on the system, then we can go to the vital site and see that actually there is a relation between the mass we we get them on the wild side between the surveys relation of this mass and the previous months we found on the Blackboard site so days again.
Regensburg: Every day relation of the two masters found. But now, the difference is, it is selected by the dynamics. So our Hamiltonian selects exactly this.
Regensburg: Relation between the two masters. So there's no additional freedom here.
Regensburg: And what we use. Furthermore, observed is that all the hematoma is we considered so far and all the other schemes, there was a symmetry between the exchange of black hole mass and white Tomas
Regensburg: And if you have the symmetry, you actually find that then also this relation, he has to
Regensburg: Respect the symmetry. So the symmetry is on the Hamiltonian level. That means also the dynamics has to be symmetric. Under this so you have also this
Regensburg: Also this relation satisfies this symmetry, from which we can conclude that the only two possible relations which are compatible with VC future sell independent permutation skater. The symmetry is either a linear
Regensburg: Relationship or an inverse relationship and the model. We are the class months we discussed in our paper.
Regensburg: Was actually one way, whether
Regensburg: Weather relation was inverse
Regensburg: Okay, with this i'm i'm done with the pattern derives those other further questions on on the first part of the talk.
Regensburg: Okay seems not so then Fabio will continue with the second part.
Regensburg: Of your body. So now in the second part of doc. I'm going to present you with these new variables that we
Regensburg: Defining this Las Vegas and try to explain why ID contractual is enough to the BB variables, who's really nice to see, although, as we would see the deprivation is
Regensburg: Not exactly the same and how these Bibles. We allows you to
Regensburg: Overcome the limitation facing the initial condition due to the presence of the top seven plus we have discussed in our in the first part of
Regensburg: So plan stand, how to go step is viable. Let's go back for a while to our priests motor that yiannis was introducing
Regensburg: In his battle to talk. So as nobody was also mentioned measuring these comments, the size of the limitation is essentially the fact that one of the momentum that we're pulling in it.
Regensburg: Was related to the righteous killer, but the proportionality factor was depending on one of the tree integration constant and he is dressed in red color.
Regensburg: So now these viable will be shared the relative to aggression mascara only if this integration is going to constantly selected to be independent of the mass and this was actually the regime of initial conditional. It was
Regensburg: Selected by the mass relation that yiannis was talking about. So now our idea was to try to go start a new set of variables which one of the main is directly related to the cash mosquito without
Regensburg: Any accoutrements of the initiative of the
Regensburg: integration constant. So there are only make people make a factor as proportionality factor. And this is the new set of bias, we introduce it and the red one here is the momentum K
Regensburg: Is exactly the face space exploration of the question Masekela in our piece of the square root of depression mosquito in our papers Bibles and we kept for simplicity. The other main to be
Regensburg: Yeah, the momentum to be exactly the same as before.
Regensburg: And this was a simplicity choice. So these for sure will communicate with the other, but
Regensburg: As we will see later, there is still like a small dependence on initial condition because of this second momentum and we were not able so far to find to get rid of this dependency these other momentum. But by the way, this will not affect the
Regensburg: Our criteria for physical variability, which is quantum effects are digging in the local bunch of achievement unique curvature upper bound in the hiker maturity.
Regensburg: But we will come back to this soon in the dog. So for the interpretation of this momentum, as I was saying, we can Lucasfilm edits.
Regensburg: Expression. Now, in terms of the medical efficient and what turns out is that have shared this can be actually related to the missing a chef mass which is the
Regensburg: Mass included into ours to spear of area made us be these here I'm using these Carly be to not confuse it with the with the beat.
Regensburg: The beat of the connection Bibles that wings in the first part of the talk.
Regensburg: And now this quantity, once we go and share it for using the solution depressions emotion, it's exactly the classical expression of those global depression mascara. We don't only there is a factor in Omega factor in between the T's just mismatch.
Regensburg: So these what these reason why we were thinking that is our Bibles to to achieve the requirement of reading our
Regensburg: Curvature upper bound without noise pollution on the masters. And so we see later, and the seasonality here, we'd be viable. So what you see is that essentially
Regensburg: From a conceptual point of view also in that case the momentum that people in my eyes, which is related to the Hubble rate.
Regensburg: Is a sec. You can relate it to the which is scale, which is the in that context, the non trivial.
Regensburg: Curvature was based i mean by that is in the game. Now he young analogy. One of the main things that led to the to the square root of the question mosquito. She's the non trivial group actually my auntie nice little sick.
Regensburg: So again we can, can I
LSU Rel: Can I make a small comment on the previous slide.
LSU Rel: So just for the audience, like you see like it is true that the way this be, and we variables are right now being introduced. They have some similarities to be and we variables in El que si but there is an important difference like an improved dynamics of El que si
LSU Rel: One starts from the new bar approach and see NP variables one uses the physical areas of the loops to regularize the field strength of the Australia Barbara connection and then one finds that being variables are natural choices were classically
LSU Rel: The relationship between Richie skeleton be appears the but the difference here is that
LSU Rel: One is not doing that construction, but one is postulating that one is choosing be essentially as a variable which is related to crush man's killer.
LSU Rel: In some way so I think like it is true that there is an analogy but one should straight there is a caveat that the way it is a personnel Qc is quite different from the way it is done here. Second. My second comment is that, though. I don't remember.
LSU Rel: Anyone using the variables. The way you have used but Christian Boomer and Kevin vendors lot in 2007 when they were trying to make a new bar scheme of Kentucky sacks. They had very similar variables, except that
LSU Rel: They didn't write in terms of freshman scholar then couple of years later, like with my student I showed that very similar variables exist again for can Tosca sex but we didn't write in terms of freshmen scholar. So that is the only two comments. I want to make
Regensburg: Yeah, thank you for this common, especially the second maybe that can be related back in only doctors formations and it will be interesting to check
Regensburg: The difference. Once the migration is performed, but he had to come back to the first comment. I agree with you. We somehow are taking inspiration from the BB viable survey to see. And now if you prefer. We are like reversing the logic. So let's start with the
Regensburg: With the current virtual environment we have at our disposal imposter viable switch
Regensburg: Me, then pulling realize that in a in an allergy to what is done in the in our community. But you're right. We are not like starting with God's standard connection Bibles and trying to
Regensburg: Put him in. I think the standard way then of course
Regensburg: It's interesting to understand how these Bibles would be relating this context. And this is something that we would like to work out in the next future
Regensburg: Is there any other comments or should I
Jorge Pullin: Just go ahead
LSU Rel: Maybe I can just make a very small comment again so
LSU Rel: Like, there were, there was a work, which I did with my students in which we looked at lots of different families of different variables possible with satisfy the improved dynamics criteria for Kentucky sacks and
LSU Rel: It turns out that there were very, very strong constraints on different sources possible. So I haven't studied this in the way you have studied now like that was a long time back
LSU Rel: But if you want like I can send you an email that paper and you can really look at whether your variables satisfy those criteria because what we found was that
LSU Rel: There was incense no choice possible which was free from one problem or another. And those were the results, which then motivated us back to New not kind of scheme which
LSU Rel: Alex courage and I did and then Javier me and obey followed generalization of that. So I think it will be look good to look at some of those papers which were written in four or five years ago and see whether your variables are free from those problems.
Regensburg: Yes. Yeah, do it will be great if you send us the reference, just let me see that here we are using a kind of new note scheme for these vials, but the corresponding scheming connection Bibles is not
Regensburg: You know scheme anymore. It would be a sort of Mubarak scheme.
LSU Rel: Yeah, so what the work which I did was, it was not just based on new not schema all kinds of new bar variables like
LSU Rel: And in that time. If you remember, they were the slightest refinement ideas were in fashion for some people and we we showed that
LSU Rel: Even if you take all those kinds of refinements possible there are very, very strong constraints on physical viability of the variables in the sense of getting the right
LSU Rel: Ultraviolet bound when single resolution happens getting right infrared scale or infrared behavior at small space time curvature and produce your cell independence.
Okay.
Regensburg: Yeah, we will show you look up at the reference that you send us
Regensburg: Thank you for doing so let's continue. Now for the classes that you have different Bibles are remarkable submission is that even if we do this. Can I got affirmation that
Regensburg: I have including. It was nice to define the viable the form of them is Donna we means accepting the same as you know what feels like most and which is a remarkably simple form of them on and where they are at Max Max quadratic
Regensburg: Dance. In the meantime, there are no invest powers of the moment. And as we see later in the door. This will will will also
Regensburg: Allow us to perform the first step in the construction of the wanting to heat up to the solution of the internet constraint as a quantum
Regensburg: So as you're honest was mentioning the first half of the dog. The analysis of the echo several what can be done in a day. So, so in this case I would be, of course we can. This as it was discussing the dating for a spot.
Regensburg: But again in classical case we have only one future selling the vendor. The observable, which actually includes both the integration constant, which are coming
Regensburg: From the solution on the dynamic and we can interpret it in terms of the black hole mass by simply reconstructing the matrix efficient in terms of the
Regensburg: Of the faith based Bibles and look for the
Regensburg: For the behavior of the matrix that is
Regensburg: isometric to the to his boss you solution if we identify on shell geese, the XML, which the with the horizon smashing the ratings. And again, by means of according to the scaling, we can
Regensburg: Only absorb reabsorb one of integration constant which we never will not enter the finance operational domain as you're honest, we're seeing in the first part of the book.
Regensburg: So now with the classical setting.
Regensburg: at our disposal. Let's go to the effective quantum theory and for the second observation is that the indigo, the black hole is essentially as the same structure of Kentucky. Suppose cosmology, when we have our homogeneous.
Regensburg: Slicing into the our direction and we can apply these techniques which are inspired by by quantum cosmology to construct the affected to you now. The for this we choose
Regensburg: To keep the structure as simple as possible. So we really mean is this momentum by means of the same function, which of course is a choice at this point. And we can ask, in principle, if other choices leads to a different conclusion but
Regensburg: This still to be explored and we use a constant polymerization skates, and to interpret this case, let's just go back to the interpretation of the moment. So as I said before,
Regensburg: One of them is related to the square root of professional skater. Which means, then it w musician scale of the key sector is essentially related to an investor, but you escape and will control the large commercial quantum effects, while the other
Regensburg: Momentum G the TI present in a nice combination with the financial say length that is independent of delusional scale financial service gaming is essentially related to the inverse power of the radius. So these implementation of this momentum will take care of
Regensburg: Small area radius quantum effects and scientists bit before he had a steam one integration constant appearing in the in the ocean value one of the momentum and this will provide some small difference in some regime of the masses as I was showing away.
Regensburg: And putting it now. In this way, the, the Glasgow and he's brilliant we get
Regensburg: The following effective ME, TONY on that. Because of the simple structure can be
Regensburg: Handled quite easy. Then we can solve the entire family dynamics analytical and hearing about the final expression of the
Regensburg: Solution in terms of the metrics coefficient and again the especially quite involved with. But I bought to just for completeness and what is important to keep in mind these leads to do in these books.
Regensburg: So first of all, the, the metric is the coefficient of the metric are where they find it over the wall, our domain, two plus and minus infinity, which means that, essentially, we will have to was importing regions.
Regensburg: And mobile. There are two or eyes and corresponding to the
Regensburg: Roots of the ego efficient and in the large mass limit, we can actually believe like the corresponding value of the area Vegas as the classical expression for the
Regensburg: Machine to reduce respectively. In terms of black hole and metal masters, if we are in the positive
Regensburg: Our range or in the negative range plus wanting production which he is not important is the specific form for this connection, but they both essentially to do once we send the optimization scale to to
Regensburg: Then they are going to be able to do as also i don't see your minimum value. And this is exactly corresponding to the space like
Regensburg: Transducers Arcturus, which will replace the classical singularity connecting the medical side with Whiteside
Regensburg: Move over a note here that dx, we are reporting here is essentially just a combination of the coordinates and the permutations key of G sector and
Regensburg: In the final form of the matrix essentially the skin will not appear because it's just like a
Regensburg: redefinition into the our company and the only relevant documentation scale instead is the one for the momentum, which was related to the to the question mascara. So, lambda in this case in the slides.
Regensburg: And again, the initial the individual constants are encoded in the true masses. So, and now both appear in the metric and we cannot get to the end of
Regensburg: One of them, as was done he stayed in the classic case. So now both will have physical meaning and as you can expect from the
Regensburg: First part of the talk. They are really did are truly acceptable related to them and they are respectively interpreted as the black hole and WHITE MASTERS
Regensburg: For computer care about the expression of the faith based function for the to Dr. Cole said bubbles and again by looking at just insulting behavior of the metric in the plus or minus infinity.
Regensburg: Regions, we get back essentially the classical machine solution when we're respectively. On one side, the origin and radius is related to the one the sable and on the other side is the other vehicles.
Regensburg: But important remark at this point is that everything up to here does not require to fix any relation between the black hole in Western Mass. So, up to now, this option independent parameters which can be freely specified
Regensburg: And to summarize what is the structure of the resulting space time from demonizing these variables here report the pedals diving that can be constructed by means of standard ways explicitly
Regensburg: And again, let me stress that the metric is defining and smooth all over the range. So, both for the interior and exterior medians.
Regensburg: Then quantum effects become irrelevant in the hypervisor regime and he's we resolve the classical singer it by mean so
Regensburg: Smooth transition surface between rapid and aren't interrupted the region, as can be seen by calculating also the expansions. For these reasons,
Regensburg: And because of the topology of the starting space time where we live our infinite our will essentially alternating topic tougher than and tighten up the divisions which we interpret this record and whiteboards, and that's indicated that he quantum effects so
Regensburg: In the local virtual machine quantum effects are negligible and we call smart sheet solution in yes and Arctic regions that allows us to interpret essentially also the
Regensburg: Those Diego stable as the synthetic ADM black and white and losses. So now we are in a position to answer our regional
Regensburg: Questions or about regarding the motivation of finding these variables, which was if or not we can achieve our criteria for physical variability without restricting the masses.
Regensburg: So our requirement was to a upper bound in the blank regime for the curvature. The Mayans and
Regensburg: To answer these for these Bibles, we started the crash muscular at the conceptual surface where it takes it to its maximum value.
Regensburg: And as you can see from the block here on the guides essentially the Christmas cake. So here is the logarithm the freshman scale out in terms of the
Regensburg: Possible values for the black hole and Michael masses on the two axes. And you can see that is all over the range of masses these quantities approximately constant
Regensburg: There is, of course, these central
Regensburg: Regions here which is some special, and we were quantifying the dis center regions as this interval and ratio of the masses, or when the ratio between black and white and Narcissus between one eight and eight.
Regensburg: And the reason why essentially this region is going to be special is because of the dependence from the International constant in the moment.
Regensburg: And these can be seen as follows. So now let's go to study with thunder.
LSU Rel: I have a question here.
LSU Rel: Do you, do you get similar results for all their collateral scales, besides the Chris Mannix Kaler lied regarding the upper bounds.
Regensburg: For this, we don't have as basic plot here.
Regensburg: But this should be also bounded
LSU Rel: By thank thanks
Regensburg: Well, they should be ready that we shot.
Regensburg: Studying the the onset of the one effects coming from Parliament is into two sectors, essentially, this is a way to explain why these
Regensburg: in Dubai between the for the mushroom mass for the ratio of the two masses was a little bit special. So here and report the blocks for the
Regensburg: Troops demonizing momentum and the red lines we refer to the policeman is it momentum key wild.
Regensburg: The blue one is the the JSON and for the true values of the black or white, to the masses corresponding to the to the boundary of that center regions in the previous night. So essentially, the one eight value in the eight value. The defense, he's essentially which one of the two
Regensburg: Kind of quantum effects is relevant first and in one case, coming from the Blackboard site. We will first see G sector quantum effects.
Regensburg: And then case as to why you're coming from the whiteboard site for the other value of the of the relation with the masters is the other way around, but in particular are. This was leading us to
Regensburg: Be fair the symmetric keys. So the one in which the black mass is equal to the white to last for the full reason. So in this case it topping up instead boat.
Regensburg: Kind of quantum effects are uniquely that in mind by the only the pronunciation scale lambda k and they both aligned to be large curvature quantum effects, as can be seen from these blocked and then wait to see this is essentially to study the the condition for
Regensburg: The, the classical regime. So this is the following conditions or the classroom at the classical equation and depression mosquito as to be much more level discounting. And this comes essentially from the requirement that
Regensburg: The argument of design will reproduce the classical argument, far from the one to my team. And here you see that only the lambda case kid appears and then this is we scale it by a
Regensburg: Ratio of the two masses. And so, in particular when the two masters or equal. There is only one kind of large perpetual scale, which gives us the onset of both quantum effects.
Regensburg: And for us, this was like a way of preparing this metric one with respect to the other. I'll do is show up for the previous slide.
Regensburg: The square root of depression mosquito is constant for most of the master relations with the only exception of this center part and we should be stiff constant but we different magnitude because of this exchange of quantum effects.
Regensburg: So now, as I said before, we can also like start to construct the quantum theory of this of this model. And this can be done by the standard step already available in the church, and in particular in the
Regensburg: In the context of Luke quantum cosmology and here just catch the main steps that should be familiar to most of you. So, which was
Regensburg: The following body of the for convenience. The following while you have the permutation escape.
Regensburg: And we need it for the full moon choice for the laps in such a way that the affected me the effective maintenance density way to object in the jungle but direction.
Regensburg: Any particular we choose the following order Inc, which is the one similar to the one for the MMR prescription you quantum cosmology and now the best case can be essentially sponsored by the states of the
Regensburg: Course of the operator corresponding to the V Bibles VG MBA, which we just talked this multiplication operator and then the translated version of the momentum we lock this displacement of eight.
Regensburg: And
Regensburg: Now we stand that choice of rescaling the
Regensburg: Way function and eliminating the Bible's we are having the final form of the available for the mechanical scenes which
Regensburg: Now, because of the audience choosing also this case, it appears that the Ziegel the Oregon State is somehow they're not is dynamical isolated and also the positive and negative
Regensburg: Branches of the disgrace back to Mark dynamically, the Catholic
Regensburg: And moreover, as it is expected from the choice of these ordering
Regensburg: An arm over for this specific form of the Internet will sleep. We can also explicitly write down the solution.
Regensburg: For the states which are independent of the Super eight or and the report eating, find out for you. Just for completeness.
Regensburg: Of course, this is just the first step into the construction of these quantum theory because now the next question would be about
Regensburg: Completing this theory by working out the physical scale product and then the physical space and then asked if we can actually deny the effective dynamics, out of these quantum theory and that for that we need to understand better the vehicle separable and look for
Regensburg: For Bitcoin states to do it over the affected Analytics. So this brings me to the conclusion of these talks. So let me summarize the results of both parts. So we're discussing any days how
Regensburg: The table can be provided for effectively members in the course, and now the study of these observable leads to increase reach on on the initial condition that are available.
Regensburg: For the physical beauty of the model.
Regensburg: And then we were asking yourself, if it is possible to construct variables which are adopted in similarity to the be viable select you see to achieve the unique URL, but your upper bound in the blank emerging and we found
Regensburg: Such kind of variables and discussing the second half of the dog and the starting pitcher of the quantum data space time is similar to be with investigation. So again, we have the similar solution via transition from blekko to at all. And we have an upper bound on virtue and
Regensburg: More quantum effects and look at what you're doing for all possible mustard. Mustard relations and, in particular, we argue that this metric case.
Regensburg: Is we've added in terms of the onset of quantum effects. And as I saw, I didn't. It was nice. The remarkably simple form of the Western and allows us to
Regensburg: Perform his PC and then it got it. The first step in constructing the fund the quantum view now it's official work. We would like SSH to complete the one, don't do it. And to understand what is the role of the vehicle service and in practice.
Regensburg: Something that has to be understood is that these do have several do not commute already the classical level so
Regensburg: These would be really interesting to understand what what is the role of these quantities and of they're not on the DVD the quantum theory and if they play some role to label like Korean states on one side or the other. Then of course we will develop this model with
Regensburg: Full quantum gravity and here again we mean essentially to the same way in which the variables are embedded in the food to a context. Maybe we can also work out a similar formulation of the food to research that these
Regensburg: Relational is possible. And then of course we will be interesting to go farther from the
Regensburg: Standpoint of view. So here is everything going to tools fagan's magic and started the course, but we'd like to go to more physical element situation like
Regensburg: Nowadays, I'm going with ongoing conditional collapse and coming back to our original motivation for ADHD. We would like to start in our higher dimensions.
Regensburg: And assembled a great yes spaces and then after that we can compare with boy, for instance prediction about similar idea solution or
Regensburg: argument against it in the holographic log affinity with this. We are not and then you will for your attention.
Florida Atlantic University: Okay, yeah, very physical questions. So in these
Florida Atlantic University: Diagrams the quantum corrected space time diagrams. There are multiple as syntactic regions.
Florida Atlantic University: Is that what we would expect physically. So is the black hole changing into a white hole and some other universe, and if so, do we have any idea what this would look like in our universe, very simple question. I don't know if you have any ideas.
Regensburg: You're asking about how to eventually
Regensburg: Like every senior to go to the whiteboard side, even if you are on the political side. Is this what you're asking.
Florida Atlantic University: Can you say it again.
So,
Regensburg: We were thinking about these in the sense of, let's say we are like an observer sitting in the region one the Blackboard site if we have any like information about
Regensburg: Also that I stopped the diagram from the side.
Florida Atlantic University: That's right. Well, if we will we see the the white hole in any way or
Florida Atlantic University: That's just in some other universe.
Regensburg: What can be shown is that for it. For instance, the Richie scale on the side actually depends on the whiteboard mass, but let's say the collection, which is really
Regensburg: Negligible
Okay.
Jorge Pullin: But also the space time, so presumably cushy horizons rise that presumably are unstable. So
I see.
Francesca - Western: Yeah, this
Regensburg: Is somehow. And the third black hole and you don't
Regensburg: Actually have a collapse of matter also excluded been our phenomena like Hawking radiation, which makes everything
Regensburg: More complicated. So this work by, for example, Valley, which shows that if you include Hawking radiation, these two regions, one in four. For example, He the same universe, for example, so
Regensburg: From that point of view, it's probably not the model itself is just not complete, to answer the question.
Florida Atlantic University: And then maybe maybe the difference in mass between the black hole and white hole would be accounted for by the Hawking radiation and maybe
I'm
Regensburg: Walking radiation is not in this patient included so
Francesca - Western: I'm
Regensburg: The principal in the interior region with this is black and white one into your region. They have a time dependent space time some principle that's how to talk about energy conservation.
Regensburg: Maybe in this missiles of the two masters by by saying that they actually might have been part of creation or something is in this tiny pendant into the region.
Florida Atlantic University: I had one other question. So I thought again about this the the action of the residual
Florida Atlantic University: And I think I understand what's going on. So the what you really had was residual coordinate transformations. And the thing is that
Florida Atlantic University: Residual coordinate transformations are the passive equivalent to do a few more films acting on everything your dynamical variables as well as the cell and
Florida Atlantic University: If you consider instead the the active different morph isms acting only on the dynamical variables and you leave the background cell not affected by the different more films, you will have a non trivial action on the face face and the condition that
Florida Atlantic University: The condition of invariance under this action on the face face will will be equivalent to independence of L not. I think that. Would you agree with that. That makes sense.
Regensburg: So first of all, it's not, not a condition that that they the same, maybe we can go back to
Regensburg: A session outcome from the computation that is
Regensburg: The a
Regensburg: Here and here are the same, but I'm not completely sure if I understood what what do you mean by leaving the producer sell
Regensburg: Unchanged
Regensburg: Background destruction of no change the background structure because that is essentially what happens here.
Regensburg: Yeah.
Florida Atlantic University: Yeah, so the thing is that here. You're doing a coordinate transformation and a coordinate transformation is equivalent to doing an act at applying an active different morph ism to all of your structures, your, your dynamical variables as well as the cell
Florida Atlantic University: So, but if you if you were to not let the different more films act on the financial cell if you would really treated as a background structure.
Florida Atlantic University: Then you would get a non trivial action on the face face.
Regensburg: Yes, that's true. But, but then you change the physical size of the cell.
Jorge Pullin: Any other questions.
LSU Rel: Yeah, I have a couple of questions. So coming back to my previous question regarding the Christmas gala. So if I understand the logic.
LSU Rel: Us. Start with a classical theory right where they only curvature 10 so that is number, any scene is the vials answer.
LSU Rel: And if I know wrong or leave your medical information will be qualify in the Christmas trailer and that is why you choose this quantity as a privilege quantity that you apologize, so that you can get an upper bound. When you go to the high quality region. However, in the quantum theory.
LSU Rel: Richie tensor is not cedar anymore, so why should Chris Mannix Kailash will play a prominent role with respect to Richie components or any other retailer that you can build since in the quantum theory.
LSU Rel: None of them are funny saying
Regensburg: Yes, but I mean we have to start from the classical
Regensburg: To eat. So we were using the ones we have available in the class that you
Regensburg: Do in the
Regensburg: In the one devious
LSU Rel: Okay, maybe I can ask obvious question in a slightly different way so that the model is built from scratch, so that the rational scale or is
LSU Rel: Going to get universally bounded and it is free from the changes in mass, the universal boundaries, free from that.
LSU Rel: But what about other curvature invariance like since the quantum theory will have a nonzero Richie Skylar their and their higher order curvature and variance and other curvature and variants of the amount answer. It's not obvious, whether they would have the same property.
Regensburg: That is true. Some principle. The other coaches skaters are
Regensburg: You
Regensburg: Know bunch of them are related by with some
Regensburg: We we do own study that in detail, you know,
LSU Rel: So just, just to then comment that in contrast to the model, which we have here and I had like, which was based on essentially on the
LSU Rel: striker Barbara connection. And again, the judicious choices motivated by several arguments of what should be the moon or scheme.
LSU Rel: Relevant for that we checked various curvature invariance. And we found that for macroscopic black holes. There were no such problems with the rescaling for any of the curvature ingredients.
Regensburg: So I mean that from the previous
Regensburg: Then no prompts occurred. Also, we expect this here, and I think we can be sure that the these two also not diverge.
Regensburg: Because essentially, there is a is a minimum bound for the be so. So there's this transition surface, which has a minimum radius. So we should not expect that the Richie scale is actually diverging at the transition surface and having just one
Regensburg: Culture as scale and bound than we expect that this is also true for the others. But you're right. We principles should check these details.
And
LSU Rel: Read the question is not about the divergence, the divergence won't talker, like, one can simply show that easily. But the question is about the rescaling freedoms and how they affect all of the curvature invariance. That is the question here.
Regensburg: In the sense of duration of the master me
LSU Rel: Yeah.
Regensburg: Okay, no, he says to be the other Mayans were to check for this.
Regensburg: For this new model for the previous one, there were
Regensburg: No problems for the relation with the mass we were fixed now for this one we analyze it.
LSU Rel: Okay, thank you. And I have one last question. So we want to compare this proposal with
LSU Rel: All their more letters you see in the arena as the Colorado variables. Is it possible to cast or to get how these Parliament parameters in that in those models that are we under taffy. That does he look like in this, in this case.
Regensburg: I was saying, you saw
Regensburg: Our new boss scheme and the duration of the automation scale are the following. So as you can see there are
Regensburg: Now,
Regensburg: Entering the game mode, the component of the connection end of the
End of PB
LSU Rel: Is it possible to give a simple geometric
LSU Rel: Explanation to this choice or
LSU Rel: Is at the moment you got that and that is not
Regensburg: What you want the buyer must point of view, we have not thought about
Regensburg: For the moment, and interpretation in these in these terms.
LSU Rel: Okay, thank you.
Jorge Pullin: Any other questions.
Fund. Ineractions, Univ. Wroclaw: One more question, if I may.
Fund. Ineractions, Univ. Wroclaw: Can you hear me.
Fund. Ineractions, Univ. Wroclaw: Essentially about the left side physical consistency of the model. Namely, we still have this
Fund. Ineractions, Univ. Wroclaw: What most of the people call in pirate regulator such that the slices that merge into slices in Kentucky starts around compact.
Fund. Ineractions, Univ. Wroclaw: And we are of course using this what you confidential. So to make it compact. And then the question is if we change physical size of this is are the results environment or is there a removal regulator remove our limits.
Fund. Ineractions, Univ. Wroclaw: Which is which gives us some well defined quantum trajectory for this particular model.
Regensburg: So the metric or the physical quantities, we get in the end. These are completely independent of traditional structure. So if you choose different
Fund. Ineractions, Univ. Wroclaw: Well, they are independent on the coordinate size. Yes, but regarding physical changes of physical sizes.
Regensburg: Depends on the depends on the integrated version which is independent of the coordinate system.
Fund. Ineractions, Univ. Wroclaw: Yeah, but I'm not asking about the coordinates.
Regensburg: It's also invariant other changes of the producers of physical size reduce yourself so
That's really
Dependent on
Fund. Ineractions, Univ. Wroclaw: physical size of the future. So really, okay.
Fund. Ineractions, Univ. Wroclaw: No more questions.
Jorge Pullin: Any others.
Jorge Pullin: Okay, let's thank the speaker again.