Jorge Pullin: Okay. So today we have a panel on quantum black holes with machine hand prancing, and LED Wilson, it will be hosted by Vicar Hussein. So, Vicar, can you take it away?
Viqar Husain: Yeah. So so thanks everyone for joining this. I'm hoping it'll be a very good discussion before I start. I just like to mention that it'd be useful if everyone waited for the 3 presentations to finish
Viqar Husain: before asking questions that way. Everyone has enough time to finish, and then, and then we can proceed hopefully to a really good discussion. So you've all seen my first slide. I just have 2 slides.
Viqar Husain: and I've put up here some questions that I have asked myself over the years.
The first is.
Viqar Husain: what does quantizing the Schwarzschild solution reveal?
Viqar Husain: And I asked that question because the shorts of solution is just one solution.
Viqar Husain: and we're looking at something much more complex in my view. So this is why I pose that question.
Viqar Husain: The second question is, when we look at effective dynamics
Viqar Husain: with perhaps just discreteness, corrections or other corrections, quantum corrections beyond just discreteness corrections.
Viqar Husain: Then the question is.
Viqar Husain: what does that reveal with matter and without matter, For example.
Viqar Husain: does it provide evidence of Black Hole to Whitehold transitions, shockwaves? What else?
Viqar Husain: And the reason I ask these questions is because, as we all know, the classical
Viqar Husain: theory of scalar field collapse is extremely well understood, both from an analytical perspective and a numerical perspective.
Viqar Husain: And one of the questions I've asked myself is, what's the quantum theory of this? So just very briefly. What we have here
Viqar Husain: in the setting is that this is going. We're going back to the early nineties.
Viqar Husain: we but there's weak data. This means that the scalar field. This is all in the asymptotically flat context and weak data means that the ATM mass is below a certain threshold.
Viqar Husain: Then the scalar field just comes in and bounces back, goes back off, and there's no black hole, which is what I mean by just scattering
Viqar Husain: and strong data is when the ATM. Mass is measured to whatever parameters in the scalar field profile that you put in is above a certain threshold, and then there's always Black Hole formation.
Viqar Husain: and then there's a transition reason between the 2, which is an extremely finely tuned, naked singularity about which a lot has been written.
Viqar Husain: So the basic question here is, what is the quantum theory.
Viqar Husain: and the broader question is, is matter necessary for a complete understanding of quantum black holes.
Viqar Husain: And so the recent work, the LED and I and our students have done is that effective theory of dust collapse may provide a hint to this bigger problem.
Viqar Husain: which is that you have some form of collapse, some type of metastable black hole.
Viqar Husain: and then some outward going burst, maybe a shock wave. And perhaps this process continues because this matter goes out. Gravity starts to pull it back in.
Viqar Husain: and so is this going to continue forever this kind of oscillation of matter collapsing and then bouncing.
Viqar Husain: So those are just 3 comments I wanted to make, and then let me just go to the next slide.
Viqar Husain: which is what our 3 panelists are going to talk about.
Viqar Husain: So first Perm will open with the Lqg. Of the Schwarzschild Solution
Viqar Husain: Interior exterior comparison of approaches and open questions.
Viqar Husain: and then machine will talk about covariant, effective dynamics
Viqar Husain: for vacuum for spherically symmetric space times, and in particular, that a solution of those equations
Viqar Husain: and some comments on the Black Hole by whole transition from this perspective.
Viqar Husain: And then, thirdly, it will talk about the recent work on Ltd. The mitochondria toll on Bondi models and dust collapse.
Viqar Husain: and how that gives this effective equations give rise to weak solutions which predict shock waves.
Viqar Husain: and how this shows dynamical singularity, resolution, and it will also talk about implications for the Information
Viqar Husain: lost problem.
Viqar Husain: So that's those are my opening remarks. And so, Baham, please take it away.
psingh: Okay.
psingh: Thank you very much for your car.
psingh: So i'm going to start with
psingh: the loop. Can everyone see my screen.
Abhay Vasant Ashtekar: Yes.
psingh: okay. So i'm going to.
psingh: I'm going to start this panel discussion essentially for making of
psingh: platform, also for motion and
psingh: at stock, which deal more with the dynamicals and stock, deal more with the dynamical scenario and motion Stock is essentially in the middle of
psingh: where I would be pitching my token network
psingh: be pitching his talk.
psingh: So i'll be discussing the work which I have done with Abbe and Javier couple of years ago, and we have been
psingh: following this trajectory, and various of the generalizations of this model have been studied.
psingh: So
psingh: let me
psingh: go to a brief introduction.
psingh: We are essentially trying to study the loop quantization of
psingh: the Crusco basically the critical space time.
psingh: And
psingh: one thing which is very useful for understanding the Schwarzschild Black Hole, shorter and tea is that it is isometric to the Kentucky sex vacuum cosmology.
psingh: And since it's a since one can choose a homogeneous slicing, as in the cosmological models.
psingh: people started applying the loop on this allergy techniques
psingh: to understand what happens
psingh: to the singularities in this, especially the central singularity in this inside the Black Hole.
psingh: Basically how does a quantum Romanian geometry
psingh: changes the space time near the similarity. What are the blank scale effects?
psingh: And the intuition was that very similar to what we will see in the we have the quantityometry effects lead to a universal bounds on space-time curvature
psingh: kind of bounce a picture of big
psingh: a similar picture about the merge
psingh: in the loop cultivation of Schwarzschild black holes, and these attempts have been going on for very long time, starting from 2,005 and sticker and volume all, and then
psingh: later on, like polymer and vendor, slow, then so on, and like many in this, especially up to like 2,018, 2,019. There has been a flood of various papers
psingh: trying to understand different models in detail.
psingh: The spatial metric is homogeneous, so that makes life easier to understand this interior, using the cosmology code
psingh: analogies. But the metric is not isotropic. It is an isotropic.
psingh: So
psingh: the Kentowski sax. If you just look at the Kentowski sex cosmology the singularity is like a cigar like the When the 11 approaches the Big Bang. In personality
psingh: the problem becomes technically challenging, because not only there is a while curvature, but also there is a spatial curvature, so an isotropy and spatial cur, which are both, are now clock together. They both play a very important role.
psingh: and that is where the conversation has been
psingh: more
psingh: difficult to understand.
psingh: So. But the physical implication has been studied by many groups.
psingh: and I'm. I'm. I really apologize if I miss some of the names, but I've tried to pull
psingh: as many names as possible.
psingh: There are 2 important caveats in.
psingh: When we try to understand this picture. The first caveat is that this is an idealized picture of an internal black hole. We are not looking at a dynamical collapse scenario.
psingh: and there is no proof yet that any of the conversations which have been studied so far they arise from a dynamical collapse scenario. So that is a in my personal viewpoint. That's an
psingh: open, unsolved problem which we still try.
psingh: which we still have to understand.
psingh: The second very important caveat is that almost all of the results which various people have obtained, including for the dynamic other situations which
psingh: Mission and Edward
psingh: talk about Later, one is assuming
psingh: the validity of an effective space-time description.
psingh: an effective continuum space time description in which one starts from classical Hamiltonian constraint and one polymerizes it and then one is trying to understand various effects
psingh: coming from this effective space and description.
psingh: We do not know how valid is this effective spacetime description for the Black Hole Space Times. But the good news is that, at least for the cosmological models when you have, while curvature, then very sophisticated simulations for wide variety of States
psingh: for
psingh: an isotropic model show that this effective space-time description is
psingh: quite accurate.
psingh: But still this this is
psingh: okay. So with this: let me come to the classical aspects. And this is the only slide which you'll have most of the equations, because i'm setting the stage.
psingh: The special manifold is our cross s 2, and this has a judicial metric which is given by this particular equation.
psingh: and one notices that there is a non-compact
psingh: X direction which
psingh: for which coordinates for L. Naught, and you have to choose a traditional cell to define the simpleactic structure, and for the cylindrical traditional cell we it
psingh: make it's volume as B. Not as 4 by R, not square. L.
psingh: Then, using this underlying symmetries, the connection and the triads, they can be written in the form of these 2 equations.
psingh: and one can choose a convenient set of variables such that the the of the the pose on brackets do not depend on are not an Ln. And the ideas, then you would choose C. And P. C. And B. And P. Be in this particular form
psingh: the moment you do that one understands that they are also rescaling properties; that under L, not going to some rescaling alpha, I will not see changes in this particular way, and Pv. Changes in this particular way, C goes to our Pb. But DC. And B. They remain invariant.
psingh: The the lesson from loop on on the smallogy and from areas of the post multiple models is that this pollution, then, should not play any role.
and
psingh: for physically relevant
psingh: of zoom, but like the freshman scalar or the ske of the white.
psingh: and so on.
psingh: and the curvature scale at the B should not depend on this alpha, and this is one of the main requirements which we can pose for
psingh: demanding a consistent conversation. And in this talk I'm. Going to talk mainly on
psingh: the how we obtain this consistent conversation, and how we how this consistent conversation compares with other schemes.
psingh: One thing to notice is that the classical horizon in this, in this
psingh: space time
psingh: corresponds to when Pb. Becomes equal to 0. PC. Becomes equal to 4 M. Square, and at the horizon B also becomes equal to 0.
psingh: Similarity Central singularity occurs at Pb. Equal to 0 and PC. Equal to 0. So whatever scheme which we want to build from, but when we try to quantize the fury, we have to be very careful. How do we choose this Delta V and Delta, c.
psingh: And I will come up with these questions down.
psingh: So
psingh: so let us look at if it if one looks at the
psingh: if one looks at the quantum aspects, the the general idea of the quantum aspects, the procedure remains very similar to what we do in the loop quantization of
psingh: homogeneous Space Times. One starts from a classical Hamiltonian constraint. One expresses those
psingh: the quantities in terms of the
psingh: connection and the flux of the triad. And then there are certain polymerizations which happen from a non local nature of the field strength, and then one is trying to understand the physics of that Hamiltonian constraint.
psingh: But different conversations are available because this is a a much more complicated scheme than a single isotopic Ilw space time. There are lots of cultivation. Ambiguities
psingh: which are also good
psingh: and different accommodations, results from different ways of expressing this curvature in terms of.
psingh: and how the smallest loop area
psingh: assign using quantum geometry. And there have been different procedures to do that. People have looked at different
psingh: based on that.
psingh: But basically, the punchline is that the quantum constraint consists of terms like this, signed delta B
psingh: by delta, B, and sign delta, c. By 10 to C with delta B is a fractional length of each link of the placket on the theta 5 to sphere and Delta, c. Is the fractional length
psingh: of the links in the X direction for the plackets in the P to X. And 5 explains in this on this
psingh: in this manifold.
psingh: Now the departure from the classical theory should only offer in the plank regime, and not when the space time curvature is small.
psingh: This is a requirement which we must put, because if you have a departure which is happening at very small space and curvature, the huge departure happening at very small space time, per which of all
psingh: a large microscopic black horse, then we know this conversation is going to be ruled out.
psingh: My observation.
psingh: So
psingh: the the point is like, as in the early days of loop on the small G, they were
so.
psingh: some oversight which were made. Similarly similar things happen in the Black Hole Space time, and slowly, as we are understood, we understand the physical implications on the phenomenology. We have been
psingh: trying to come to the night model.
psingh: So that is why I put them there many pitfalls, even though the models may seem non singular, so you may start from some delta V and delta, c. Of your liking, like simplest choice being let us put Delta V and Delta, c. As some constants numerical constants. And when you write down the quantum constraint, and that will look like a
psingh: finite difference equation, Which will you? And you may think about. This equation is non-singular.
psingh: That does not imply that you really have a
psingh: physically consistent picture, because it can happen that you may have
psingh: very large space
psingh: coming from the these polymerization terms, even when you expect that
psingh: you should not have, and you may.
psingh: Your model may be just ruled out by observations.
psingh: So
psingh: we are some of the questions one can post. Is space-time curvature at singularity resolution universal
psingh: or
psingh: If it is not universal, how does it scale with the mass of the blackboard.
psingh: Finally, we would like it to be universal.
psingh: because we have seen a very similar thing happens in group on the smallest. We have the energy density at the bounce turns out to be universal.
psingh: But
psingh: if it's not universal, how does it scale that mass? Certainly we do not want to have a scenario or a model, where, if you take a very large mask, then the scale
psingh: yeah, it goes inversely with mass or some other inverse power with mass.
psingh: one very important property, and and this which which we need to understand in this model, and this model gives us a very unique opportunity to
psingh: bring this out is to loop quantum effects, distinguish physical versus the coordinate similarity.
psingh: So in this picture, which we have, we have a central singularity inside the blackboard, but at the horizon. And these coordinates there is also coordinate similarity.
psingh: But we know that just a coordinate singularity it is. It is pretty easy to write down a wrong polymerization scheme which does not distinguish the central singularity
psingh: and the partner similarity in the sense
psingh: that it, the plank scale effects will be also seen at the central singularity, and they are quantum gravity effects also the boarding and singularity.
psingh: so
psingh: it's not built in, as if if you think slightly. It it is easy to realize a group of gravity
psingh: is not built in to really distinguish these 2. You can. You can easily make a mistake here, because one is essentially looking at the whole of the connection which is proportional to the extensive curvature, the globe in the extensive coverage it does not translate to the blow in the crash on scalar always, and so on, so there can be an ambiguity there. So this is a very important point.
psingh: and then the next question is that Well, even if you have a checkm for the first 2, how symmetric is the P. Or me is your bounce so asymmetric that you start from a black hole.
psingh: and let us say which is solar mass.
psingh: And then on the other side, if there is a bound, you can
psingh: bring all the white out, which is extremely extremely massive. And how does that happen? So there are many pitfalls and requirements. One can
psingh: what one can put for a consistent quantization. Some of them, you may say, like they are probably more demanding like.
psingh: and some of them are really like necessary things like you. Should one should be able to distinguish physical versus coordinate effects
psingh: and better.
psingh: How do you have models which are rolled out by
psingh: observations?
psingh: Okay. So
psingh: Now i'll briefly talk about a prescription which is based on the transition service, and this was the word
psingh: which I didn't
psingh: and Javier
psingh: couple of years ago.
psingh: The idea is that if you to choose Delta, B and Delta, C in this prescription as G. Rock observers.
psingh: then all the face based functions which are constants along dynamical trajectories. Then
psingh: each you can show analytically that each solution is identified by a transition surface.
psingh: This charity which occurs at this particular
psingh: time, and then it joins a Black Hole region with the white whole region.
psingh: This can be shown analytically, assuming the validity of effective dynamics. In all regimes this can be shown. You do not need nomadics to show this.
psingh: So the idea which we proposed was that we consider plackets on the transition surface
psingh: when the curvature invariance. Take the largest value, because we know that curvature invariance take largest value at the transition surface.
psingh: and then we.
psingh: using that transition surface as a guide and the plackets on the transition surface as the right, we determine what should be Delta, B
psingh: and Delta, C,
psingh: basically the physical fractional area for the analysts around equators computed at this transition surface determines the relation between Delta, C. Delta, V and Pb. As
psingh: if this capital dies down, which is the minimum area coming from quantum geometry
psingh: and the physical fractional area of 2 sphere of the transition service gives you another relation, and then
psingh: for very large blackpools. This gives you
psingh: the relation of Delta, B and M. And Delta, C. And I'm. In this way.
psingh: then, we can compute the physics of the resulting model with the previous approaches, and here I am plotting one of the one of the relevant on observables. Pb. Versus
psingh: the Time Capital, T.
psingh: And I'm. Plotting various models here. So I have
psingh: done.
psingh: Dashed go this dotted curve, which is the Gr, which is this very faint line going like this from here and at this capital t equal to 0. There is this classical horizon. So it starts from here, and then this line goes in this direction, and the classical singularity will be read somewhere.
Yeah.
psingh: then, there is a
psingh: Aos model which is the model I'm talking about in this. This is given by this dashed line like this: One starts from the classical
psingh: horizon.
psingh: and then there is a bounce, and then one reaches
psingh: White hole like region on the other side.
psingh: Then i'm up, comparing them with 2 other approaches, which one of the approaches is called this, which I gave it
psingh: Alex. A few years ago. The Cs approach Cs approach has some similarities. With this as of Aos approach.
psingh: And what happens is that this is given by this dash dotted line, but much later on, much much later on it will bounce, and then it will go into
psingh: a much larger
psingh: anti-track region, or a much larger white whole region.
psingh: The difference between the Cs approach and Aos approaches essentially
psingh: that the Cs approach
psingh: has a very symmetric bounds, and then the richer scalar is such that
psingh: at for very large macroscopic black holes, this the way to scale it becomes extremely small. That is not the case with the Us. Approach.
psingh: and the other approach is this Bv approach, which is the Boimer vendors loop model, which was inspired by the improved dynamics in Loop, one of the smallaging.
psingh: But this model has
psingh: various problems, including near the horizon, and later on, so you can see, like even near the horizon, like there is. It's really disappointed
psingh: to the horizon. But if you are away from this classical horizon. Then what happens is that after the bounds it goes into a
psingh: series of
psingh: bounces, and it doesn't really go into an anti-track region. But this space time for response to a
psingh: constant curvature.
psingh: a product of concept which are spaces which is essentially like, which can be written as an effective charge in AI
psingh: space time. The problem is that as you
psingh: and after the pounds one cannot really trust this effective description much because one reaches the scales of PC. Which are much smaller than in on the Area gap, and then the fluctuations will become large, and we do not know how well it is this effective picture.
Viqar Husain: my firm. You have a couple of minutes.
psingh: Okay, so I will just come to the curvature Invariance, and then the Aos picture would turn. One can show that the curvature invariance
psingh: for this leading order term is a is is composed of a fundamental constants. We have this capital that I is essentially like gamma and healthy, and the connection terms go as M. Square, and you can see that the freshman scalar versus T. Takes this universal value here.
psingh: and one can also extend this picture outside to the exterior. Now, in the exterior there is no homogeneous, homogeneous, spatial, slicing, but one can take time like hyper surfaces. And one can take this 3 metric with minus plus signatures.
psingh: The cost is that one has to work with now connections and clients which are su 1 one value, and following the same strategy 1 one uses in the interior for Delta, V and Delta, c. One can
psingh: One can also explode the exterior of which various detailed asymptotic properties have been studied. There is a as in product limit, but there are some we quantum corrections which are attained, and the fall of
psingh: What was that?
psingh: One or 4
psingh: so essentially like? The picture in the middle is like a If you look at this middle diamond here, there is this black Hole space time. This green dotted line is the transition surface. The the past of this black hole is to send the the trap
psingh: correct by
psingh: the the past of the Stammon is a trap Service the future of this time, and it's the end. Trap surface, and it keeps on repeating.
psingh: And this is a this is for very large microscopic black holes, and that is why we get a very symmetric picture
psingh: cool.
psingh: So let me just summarize
psingh: the basically the lessons we have in from the loop foundation of the Schwarzschild Space Time are many, and
psingh: unfortunately, like it is very difficult to summarize. In 10 min, 1015 min all the developments. So i'm just focused on the few main points.
psingh: The main point is that the loop foundation of social space time is a pretty problem, because it's a while plus spatial curvature coming together, and we do not have that kind of
psingh: quantization. Yet even in the loop one of the smaller.
psingh: There there is the Yankee 9 is not fully done there.
psingh: so ideas which have been quite successful in Lqc. They have to be used with caution. One cannot just arbitrarily assume that improved dynamics will work in this case
psingh: it that fails very badly when one sees that, and that is, I think that is because we have really not understood how to apply it
psingh: properly.
psingh: The Aos prescription, guided by effective dynamics, provides a consistent picture of the physics. It passes various tests for viability based on that. Many other models have been Refinements have been developed which have been studied by various people.
psingh: There is an there exists an infinite number of trapped and entrepreneurs.
psingh: and these are consecutive as in protect regions, having the identical atmosphere. And this is in contrast with the polymer vendor. When it's loop stream, in which there is no such possibility. But one gets a charge in a.
psingh: The television scale has an upper bound at the transition surface. And this is this terms out of, independent of the mass of the black hole for microscopic black horse, and the Gr. Is covered in no provision agents, I think, for me personally, the most important lesson
psingh: doing even one people miss about. We are just looking at a tunnel black Hole, and it's a simpler situation. It's really not like it's it. It merges many complicated things together.
psingh: and one has really gained lot of lessons for which cultivation, prescription will work, which moderation, prescription will not work, and that is, by demanding this physical and phenomenological consistency which has guided
psingh: is foundation.
psingh: The open question remains: what happens in the dynamical collapse scenarios.
psingh: and
psingh: what and whether we recover such a scheme
psingh: after
psingh: a black hole has for
psingh: I will stop here. Thank you.
Muxin Han: Should I start?
Viqar Husain: Yes, please.
Muxin Han: Okay.
Muxin Han: Screen.
Muxin Han: Yeah, we can see it. Okay, Thank you.
Muxin Han: Okay. So so
Muxin Han: So here this is my
Muxin Han: discussion on effective dynamics. So in this, in this short talk i'm going to talk about basically 2 stories closely related. Firstly.
Muxin Han: I will talk about covariant new bars scheme, effective dynamics of the spherical symmetric loop on gravity. This is a new result, and also the second story is I'm. Going to talk about a a even newer result on the full effective space time of the Black Hole Whitehole transition.
Muxin Han: So, firstly, about effective dynamics. So i'm. Most of this talk will focus on effective dynamics.
Muxin Han: So just for an overview. So they are. They are 2 categories of affecting models in you the pong ready black holes.
Muxin Han: So far, so the the first categories are models based on the Kantowski Saxon variation, and these models has only finitely my number of degree of freedom because of the large symmetry like a Peram just to topped because the Kantowski saxophone there is a a homogeneous symmetry
Muxin Han: then, and the slides is homogeneous, so there's a large symmetry in the end. After seemingly reduction. These models are only have finite number of a degree of freedom, and well in particular, the the model talks just talked about Peram, this Aos model. This belongs to this category.
Muxin Han: and and there is another category, the second category. Can these models that reduce 40 gravity only by spherical symmetry? You know, result, using the homogeneous license, and those models are generally generally 1 one, plus one dimensional field series, and they are. They have 5 infinite many degree of freedom.
Muxin Han: and these models are are including those references.
Muxin Han: And and these field theory models has less symmetry, because so symmetry, reduction only respect to spiritual symmetry.
Muxin Han: but because they are Field Series. So they are. They have richer in principle. They should have richer dynamical properties. And so here we are going to focus on the the model in the second category.
Muxin Han: and the the new results is that we have a new scheme of effective dynamics, what we call a covariant new bar scheme, and this is the effective Hamiltonian that we propose very, very recently last year.
Muxin Han: And so here some explanation for these for this Hamiltonian. So so, firstly, it depend on the canonical Variables, Exefi, and the accounting and moment I. T. X. And K. 5, and they are the the standard phase based variables for spherical symmetric con gravity.
Muxin Han: And here this ex, if I are a relay relay relay relating to the spherical symmetry metrics. So this is a general spherical, specific, metric.
Muxin Han: and here the congregate. Momenta and k-fi appear in this Hamiltonian by so-called a new of our hormones. So these are standard numer type for all of these that we use all the time for for for black holes, for spherical symmetric l, 2, G.
Muxin Han: A. And so you can see that this Hamiltonian depend on the X and the K-fi. Only through those new bar follow me. And also you can check that this Hamiltonian go back to the ATM Hamiltonian when this delta goes to 0, and we start out. We should understand as a as the the minimal area gap in lupon gravity.
Muxin Han: And this Hamiltonian. Importantly, this Hamiltonian is not a Hamiltonian constraint, but it is a true Hamiltonian. So so this Hamiltonian in principle
Muxin Han: it it should be defined on certain, reveals space space. And this Ex. If I. T. S. K-fi are canonical audience of the reduced space base, this Hamiltonian is really a 200 and not a constraint.
Muxin Han: and the effective having the effective dynamics is given by the Hamiltonian equation. With respect to this covariance you are effective dynamics, effective Hamiltonian.
Muxin Han: and these equations are partial, differential equations on one plus one dimensions. And so the this is a a effective theory in in 2, dimensional, in in 2 dimensions
Muxin Han: and in another important property is that this effective dynamics is generally covariant.
Muxin Han: Yeah. And although it's, it's formulated in in the Hamiltonian formulation. But there is a a covariance behind this Hamiltonian, and you can derive this. Come to me by using Covariance. In that I will show in the next slide.
Muxin Han: And this is important because there has been a a long debate on the covariance of effective dynamics in upon gravity, because usually the the effective dynamics are formulated. Using Hamiltonian formulation. It is not so manifest that those formulations are are covariant.
Muxin Han: and these are some researchers for this long debate. But here I think we are able to show that and for these effective dynamics. This is really covariant, because well, there is a there is a lagrangian and manifestly covariant in the ground team behind it.
Muxin Han: So so this is
Muxin Han: this is the the log around them, behind the effective Hamiltonian. This is so-called mimatic gravity lagrangian.
Muxin Han: and it has certain higher derivative interactions. And this is the general expression of these of the Lagrangian.
Muxin Han: and it has the field Contents are, firstly, the metric gravity.
Muxin Han: and they a additional scalar field, what they call me thating scalar, and there is also a log on the multiplier, and this loginary multiplier imposing it's, used to impose certain domestic constraints, something some constraint on theatic constraint.
Muxin Han: And what is interesting is is that there is a a potential
Muxin Han: containing all the higher derivative interactions. Now it's, it's it's function of Taiwan type 2. So this chi one is a box of I and T. 2 is finding new new, and this by menu, is second derivative. Of a scalar field 5. So so for this kind tool it already contained 4 4 derivatives.
Muxin Han: right? And so these these ofi are some functions
Muxin Han: of taiwan and Kai tool. So it's keep lots of higher derivative interactions.
Muxin Han: and because you can see that when a Phi goes to 0, if go back to the known case, that gravity coupled to 9 notation dust, and this is the standard set up for the parameters for everything.
Muxin Han: And in this, when we, a couple of gravity to 9 to 9 rotational dust, and you can use this scalar field to to perform as a clock field. And that is also what we are going to do is that this scalar field file is a clock field that defines the internal time
Muxin Han: of the system. Yeah. And then, with respect to this internal time, you can de parameterize gravity and formulate the the physical Hamiltonian.
Muxin Han: And this is exactly what we did.
Muxin Han: that by by using the formation with this internal time, by using the constant 5 variation, and we can perform the Hamiltonian analysis with back to this valuation
Muxin Han: and the Hamiltonian analysis of this Lagrangian with spherical symmetry, give it to precisely the Covariance, the new wire scheme Hamiltonian that I showed in the in the last slide.
Yeah.
Muxin Han: And then this Hamiltonian equation of the covariant Hamiltonian Covariance and Hamiltonian is equivalent to the mumatic gravity equation of motion. If you perform vibrational principle of this action, you will just get the same official motion as the effective dynamics.
Muxin Han: and then the the this vacuum Hamiltonian is coming from the Hamiltonian and analysis with respect to the constant fire slice.
Muxin Han: and it's generates the time, translation.
respect to the internal time 5.
Muxin Han: And what is interesting, here is a dual role played by this by this scalar field file. So, on one hand, it is serving as a clock field and help us to department trials on this system; and, secondly, the the higher derivative
Muxin Han: interaction mediated by this scale of 5,
Muxin Han: and precisely results in the new boss scheme polymerization, and it keeps the whole me corrections in the Mubarak scheme. So what we call holomi corrections in the Hamiltonian formulation are actually the the higher the derivative of interactions in the in the.
Muxin Han: And so here, by relating this Hamiltonian to the covariant Lagrangian. We see that this new bars in the effective dynamics of spherical symmetry look on. Gravity is in this generally covariant
Muxin Han: because it is manifest at the level of.
Muxin Han: and it also suggests that the micro mmetic gravity Lagrangian is the effective lagrangian of loop on gravity.
Muxin Han: at least in the spherical symmetric setup.
Muxin Han: Okay, and, by the way, this this kind of idea is not completely new. It is already a point out by some early literature, by by Macron and collaborators, and also Karim and his collaborators. So here we are able to realize it in in the in the spherical symmetric
black hole.
Muxin Han: spherical symmetric on. Grab it
Muxin Han: All right. So let's look at the effective dynamics, for by looking at some special solutions. So here we can solve those effective equations and with yeah, with some semi-free assumption.
Muxin Han: and to get some analog of the Schwarzschild Black hole. So here we are going to assume a global killing field. And this killing field is time like and outside the keeping Verizon.
Muxin Han: Yeah. And secondly, we are going to impose asymptotic Schwarzschild boundary condition far away from the Black Hole.
Muxin Han: So with these 2 assumptions we are able to uniquely determine the solution. And this is the spacetime effective spacetime given by this solution. So you can see that this is, the solution is very different from the the Aos mode also. But this is, I think, this is a feature from the new bar
regularization.
Muxin Han: You are polymerization.
Muxin Han: and and here, so, so there are 3 important features. So, firstly, the spacetime is singularity free.
Muxin Han: and and there is a complete future infinity, and by the future infinity of the Black Hole approach asymptotically to the narrative. Elementary Ds. 2 across as 2. And this is the picture. This kind of picture is very similar to the the earlier model by by polymer and bundle's, not one that smooth
Muxin Han: also here that we are free of all the problem of that model, so, as far as I mentioned, there was model that it it give large quantum correction at the horizon, and also it keeps the the the area of the se or smaller than the area gap. And those problems are are not here.
Muxin Han: Yeah, it's an
Muxin Han: okay. And so these space-time is really complete. And and furthermore, this spacetime has companies where, plus
Muxin Han: yeah, and it contain 2 cars, and there is a standard scribe plus corresponding to the affinity of the commercial space time, and there is also a space like right plus, and and which is the square plus of of the the digital space.
Muxin Han: And because of because there's no event, Verizon, but they are kidding providers, and and those are the Keying horizons are still there.
Muxin Han: and here the holiday corrections is negligible as a cleaning price it means that at the low curvature regime and this this solution are are semi-casco.
Muxin Han: Okay, so these are the some one simple solution coming from the effective equation. But, as I said, and this effective equation is a one plus one dimensional field theory, it in principle it contains much more than one.
Muxin Han: These much more dynamical solutions. And then this is something actually open and to be understood is is how to go beyond the killing symmetry. And I understand the dynamical equation, understand the researcher dynamical poverty.
Muxin Han: and and to get the the dynamical effect in spacetime, you will see in the next slide that indeed, we need a dynamical space time to to understand, for example.
Muxin Han: And this is the the the second story that i'm going to talk about is, it is a new result, and that I I obtain with with cargo really, and and and and his student flash it.
Muxin Han: And and this model is also a closely relates to to some earlier work by by Youriculumodowski in Gamma, Yang, and John.
Muxin Han: and and here we or 10 a a really a full picture
Muxin Han: of black holes. Why call transition without using the effective equation? Yeah.
Muxin Han: Last, largely, we saw using that equation.
Muxin Han: And then this, this spacetime. So this is the parallel diagram of of the of the entire space time, of entire geometry, of of blackboard Wifi foundation.
Muxin Han: And so here it contains everything. The the spacetime includes the the gravitational collapse of the star. So there is a gravitational collapse of the star.
Muxin Han: and there is a black hole horizon. So this is a black hole horizon. This is a black hole. Horizon is transit between white for Black Hole, and it has a single asymptotic region.
Muxin Han: Okay, it has a single asymptotic region.
Muxin Han: Yeah, and also it has to be region.
Muxin Han: This is dynamical region, joining between Black Hole, transiting between black over and whiteful transition, and it used to be sync that this. This B region is a mystery that is highly dynamical.
Muxin Han: And but right now we show that there is a metric. There is an effective matrix. We all define regular in in this in this region.
Muxin Han: Okay. So so in the end we get a full effective, that effective, metric, effective geometry of the entire Black hole for transition space time.
Muxin Han: Yeah. So here the construction of geometry involves the junction condition with the star, the killing symmetry, and the interpolation of geometry in the B region, but the effective equation is not used. Also it's it's it's used the inside star, but not outside the stuff.
Muxin Han: So here it contained some key properties that, firstly, the gravitational collapse.
Muxin Han: It is homogeneous, and pressure is a, and it is governed by Lqc. Effective equation, and it gives a symmetric bounce
Muxin Han: and outside Star, and there is a regular infected metric cover, the entire vacuum space-time, and gives the black hole white Hope foundation.
Muxin Han: and in particular there is a regular metric in the region B, which was a mystery before.
Muxin Han: and and this this region B has a, and has the black hole like Horizon trans it to to Whitehole. Right?
Muxin Han: That's why this is highly dynamical. It's a highly dynamical metric inside the
Muxin Han: and outside the star there is a killing symmetry.
Muxin Han: We're, and there is a killing symmetry everywhere except in the region B, and the key in symmetry is broken in the dynamical region. B. But you know, As I said, there is a regular metric inside.
Muxin Han: All right. Let's come to the conclusion and and questions. So here I I showed 2 stories. On one hand we have a effective dynamics.
Muxin Han: which is nice, generally covariant. And this is dynamical, and it's one dimensional it's one plus one-dimensional field theory containing the reach dynamic in principle, contains reach dynamical information.
Muxin Han: On the other hand, we have a full spacetime of blackboard whitehole transition, and although these full spacetime geometry doesn't really use the the fact that the at the at the backing part of this full space time doesn't really use the fact, the equation.
Muxin Han: Yeah. And this is constructed by using symmetry, considerations, and some interpolation technique.
Muxin Han: And then about this this: this is really a full space time containing the B region and this B region it is dynamical relates to quantum effect.
Muxin Han: but it has a regular effective metric in time inside.
Muxin Han: and so it suggests that there should be some effectively dynamics. The effective description
Muxin Han: we'll see in this region. B:
Muxin Han: We're the dynamic. Yeah. So the dynamical, the effective dynamics should be valid inside.
Muxin Han: Then the question is how to relate this to perspective, namely, how to really derive the full picture of black holes. Whitehole transition from the attractive dynamics really gives the effective dynamics. It keeps the effective block around them, where, in fact, the Hamiltonian write down the equation really derived from top to down
Muxin Han: these black hole whiteboard transition, the full spacetime of black-hole transition.
Muxin Han: This is the first interesting, interesting question in my mind, and, secondly.
Muxin Han: even more interesting is that how to implement the hawking radiation and back reaction to the Black Hole, Whitehole transition and effective dynamics.
Muxin Han: Yeah, I think that's all I want to say. Thank you.
Viqar Husain: Okay, thanks.
Viqar Husain: You want to start, please.
Viqar Husain: Thanks.
Edward Wilson-Ewing: All right. Do you see my screen?
Abhay Vasant Ashtekar: Yes.
Edward Wilson-Ewing: alright, okay. So I scored, too, so i'll try and be a little bit fast, so we can have a little bit more time for discussion. So, for my part of the panel, I want to present some work that did with the car, Jared, and
Edward Wilson-Ewing: which concerns Black Hole collapse in L on gravity.
Edward Wilson-Ewing: So this will very much build on what prom and we should have talked about
Edward Wilson-Ewing: so hopefully. All 3 parts will fit together nicely.
Edward Wilson-Ewing: Let me just mention that there are 2 outstanding problems for for black holes. One is the singular problem. One is the information loss problem, I think, in loop quantum gravity. We have
Edward Wilson-Ewing: a reasonably good understanding of how the singularity is resolved. It's replaced by non singular bounce. Some of the details still remain to be ironed out, but I think
Edward Wilson-Ewing: at a qualitative level. We understand this reasonably well.
Edward Wilson-Ewing: but we know a little bit less about the information loss problem. So I also want to talk a little bit about this. Towards the end of my talk
Edward Wilson-Ewing: in the work that we did, our goal was to understand how quantum gravity effects show up in black whole models starting from the initial collapse. And
Edward Wilson-Ewing: there were 2 reasons that we
Edward Wilson-Ewing: we wanted to really focus on collapse models. So the first one was that we were interested to see how the singularity is avoided dynamically.
Edward Wilson-Ewing: So
Edward Wilson-Ewing: if you really start with a space time where you have some distribution of matter which is completely non-singular. Then.
Edward Wilson-Ewing: if this distribution collapses forms the black hole, then presumably the singular will be avoided dynamically. We wanted to get a good understanding of how that may happen.
Edward Wilson-Ewing: The other thing that we were interested in was the role of matter. So if you have a
Edward Wilson-Ewing: a black hole in classical gr, you have a singularity, so your matter will eventually hit the singularity and essentially disappear. But if you don't have a singularity, could stick around, it could play an important role.
Edward Wilson-Ewing: and in particular, when you look at collapse models, you notice that there's an inner horizon that forms, and this is something which is missed in vacuum. And so this could be something that's important to
Edward Wilson-Ewing: to include and to study. So to look at these collapse models, we decide just to start with the very simplest case which is the lemmite, toleman, bonnie space time. So these are spherically symmetric space times with a dust field. So this is pretty much the simplest collapse model that you can have.
Edward Wilson-Ewing: and of course the goal is to eventually build towards more realistic things. Where you have matter fields which may be more, they capture more of the physics that you would expect that may be relevant during collapse. But a dust field is very simple, and it provides a very good starting point to study these questions.
Edward Wilson-Ewing: There's been a lot of work studying black holes in quantum gravity and prom, and we should have both discussed some of those works.
Edward Wilson-Ewing: What we did. Of course we built on everything that came before, and I think 3 of the key ingredients that we used was first. We wanted to Hamiltonian treatment to the full space time, so not just to focus on the interior, but everything all at once.
Edward Wilson-Ewing: We also wanted to use the same improved dynamics that are used as in lu quantum cosmology, and we also wanted to include matter with local degrees of freedom.
Edward Wilson-Ewing: So these were all things that had been considered separately. But I think that this was the first time with all these
Edward Wilson-Ewing: things are put together for the first time. More recently there's also been some other work that's very complementary to this, and so we shouldn't talked about some of that.
Edward Wilson-Ewing: So let me explain the main steps that we followed to study these collapse models. I'm going to skip a lot of the details just
Edward Wilson-Ewing: for lack of time. But of course, if you have any questions, I'll be happy to answer them, and also all the details are included in the papers.
Edward Wilson-Ewing: So
Edward Wilson-Ewing: the first thing that we did was to start with classical Gr in the Hamiltonian framework and impose spherical symmetry.
Edward Wilson-Ewing: Once we have that we have 2 constraints that are left. We have the scalar constraint and the radial. If You' more physical constraint, and we gauge, fix both of these
Edward Wilson-Ewing: we use the dust field as a clock, so this gauge fixes the scalar constraint, and we gauge fix the diffusion constraint by using aerial gauge this is setting this pre-factor here to be X squared, and similarly getting this pre-factor review One is the when we use the dust time gauge.
Edward Wilson-Ewing: So this is something which is done classically.
Edward Wilson-Ewing: Then, once we have our resulting theory, we have one
Edward Wilson-Ewing: true physical Hamiltonian that's left. This is exactly as Motion was saying. We've gotten rid of the constraints. We have one true physical Hamiltonian, still the classic level we discretize in the radial direction.
Edward Wilson-Ewing: So this will allow us to proceed to the quantum theory more easily, with a finite number of degrees of freedom.
Edward Wilson-Ewing: Then we do a loop quantization.
Edward Wilson-Ewing: The economies that we want to look at are holonomy that travel along edges on the surface of a sphere.
Edward Wilson-Ewing: So in this case Mubar turns out to be a coordinate, that is an angle.
Edward Wilson-Ewing: And so
Edward Wilson-Ewing: the input that we get from the improved dynamics is that we want the physical length of this edge to be equal to the plank length. Essentially.
Edward Wilson-Ewing: And so if we want the length of this arc to be the plank length, and this is the arc of at some radius x, and that means that we have to choose an angle new bar, which is given by the plank length divided by X.
Edward Wilson-Ewing: So once we make that choice that selects me bar for us, and then we can go ahead and do the standard loop quantization
Edward Wilson-Ewing: again. As I said, we discretize along the readable coordinates. So at each node on the lattice. We can do loop quantization. They are using this. You've our scheme.
Edward Wilson-Ewing: Once we have our quantum theory, we can get some effective dynamics.
Edward Wilson-Ewing: This is still effective dynamics on this lattice that we introduced.
Edward Wilson-Ewing: and then we take the continuum limit from that.
Edward Wilson-Ewing: So this gives us an effective dynamics that describes a continuum
Edward Wilson-Ewing: space time at this point.
Edward Wilson-Ewing: Okay, so these are the main steps. As I said, I've skipped over a lot of technicalities here, but hopefully, this gives a a clear idea of the process that we followed.
Edward Wilson-Ewing: Now I won't show you the effective equations in themselves. They're not especially illuminating.
Edward Wilson-Ewing: but as usual. They're generated by Hamiltonian density, because now we have local degrees of freedom in the radial direction. Of course, our Hamiltonian is no longer global, but really is a local quantity.
Edward Wilson-Ewing: Now it turns out that there is a class of solutions which is particularly simple. So these are the ones that we focused on first.
Edward Wilson-Ewing: and those are the ones where you have this pre-factor here to be one.
This is a consistent
Edward Wilson-Ewing: class of of solutions that we get from the effective dynamics. It solves the equations of motion, and this type of solution is preserved dynamically.
Edward Wilson-Ewing: So this really is a viable class of solutions
Edward Wilson-Ewing: for the effective dynamics that we get.
Edward Wilson-Ewing: There are other solutions out there also. They're more complicated.
Edward Wilson-Ewing: That that's the topic of current work right now that we're looking at. But what i'll talk about today is really looking at this particular class of solutions.
Edward Wilson-Ewing: which still, as we'll see, is very rich, and allows us to really study a wide range of collapse models.
Edward Wilson-Ewing: Once we do this, we only have one variable left, which is B. So this is the component of the connection in angular directions.
Edward Wilson-Ewing: and the dynamics which come from the Hamiltonian density are a this nonlinear wave equation which I show here.
Edward Wilson-Ewing: The specific form is not so important.
Edward Wilson-Ewing: What I really want you to see is that this is an equation of motion which comes from the effective dynamics.
Edward Wilson-Ewing: and it's a nonlinear wave equation for B.
You. You can see that there's the polymerization that occurs here.
Edward Wilson-Ewing: But the main the main message
Edward Wilson-Ewing: to take from here is really that we have a nonlinear wave equation.
Edward Wilson-Ewing: and in general, when we have a nonlinear wave equation, then often it's necessary to look for week solutions.
Edward Wilson-Ewing: So let me say a little bit about weak solutions before I come back and talk about the solutions that we find
Edward Wilson-Ewing: to this.
Edward Wilson-Ewing: Now, when you have
a pde.
Edward Wilson-Ewing: which is nonlinear. Then, As I said, we often have to look for week solutions, and these are solutions that are not differentiable. So, just by definition, they can't solve a differential equation.
Edward Wilson-Ewing: But if you take your differential equation and you rewrite it as an integral equation.
Edward Wilson-Ewing: then a weak solution can satisfy that.
Edward Wilson-Ewing: So, for example, take a general conservation equation of this form, and integrate it with respect to both T. And X.
Edward Wilson-Ewing: So here you have a time derivative so when you integrate with respect to T, you'll just get some boundary terms.
Edward Wilson-Ewing: and then you integrate with X, and you have this integral here.
Edward Wilson-Ewing: Similarly, you have the second term here. We integrate. With respect to X. You get boundary terms in terms of F here, and then you integrate with respect to T.
Edward Wilson-Ewing: So you rewrite this Pde as an integral equation.
Edward Wilson-Ewing: And now
Edward Wilson-Ewing: it's possible for
Edward Wilson-Ewing: functions you which are not differentiable to satisfy the interval equation. So
Edward Wilson-Ewing: solutions of this type are known as week solutions.
Edward Wilson-Ewing: and in some cases you get some week solutions which are actually discontinuous. And then the discontinuity is called a shock wave.
Edward Wilson-Ewing: And just to
Edward Wilson-Ewing: I I realize that in in gravity we're not used to looking at weak solutions, but the these have been considered in general relativity. So a simple example are the thin shell solutions that you get using Israel's Junction conditions as well as the Dr. To of Shock wave.
Edward Wilson-Ewing: There's also been some work in the mathematical relativity, literature. Looking at Ltb. Space Times already classical Gr. That argues that week solutions should be considered in this context.
Edward Wilson-Ewing: so it perhaps it's not too surprising
Edward Wilson-Ewing: that week solutions would be relevant. Also, when we include fun and grab the effects.
Edward Wilson-Ewing: So what we did is that we looked for week solutions to the nonlinear wave equation. I showed you earlier.
Edward Wilson-Ewing: and in some cases for very simple configurations. You can use some analytical methods. And so we did that for a thin shell, and also an Oppenheimer Snyder collapse.
Edward Wilson-Ewing: But
Edward Wilson-Ewing: in general we really have to go to numerics. And so for that we use the garden of algorithm this is a well known algorithm that's used a lot, for example, in fluid dynamics
Edward Wilson-Ewing: and essentially is very well suited to handle these nonlinear Pds.
Edward Wilson-Ewing: Okay, so let me show you an example of what we get.
This is
Edward Wilson-Ewing: that so? The top plot shows the energy density. So this is something that looks a little bit like a star. We have a large energy density here, and then it gets smaller, and then eventually gets quite small here. So you have something that looks a little bit like starve some radius, something like this, with maybe some desk, a little bit of desk that remains outside
Edward Wilson-Ewing: the bottom plot shows the outgoing null expansion.
Edward Wilson-Ewing: And so this will go to 0 where there is a horizon.
Edward Wilson-Ewing: So as I play the movie, this this this star will collapse.
Edward Wilson-Ewing: So the the dust will fall inwards. This it will get larger inside, and Verizon will form, and eventually we will see that there is a bounce that happens.
Edward Wilson-Ewing: So
Edward Wilson-Ewing: let me just go back a little bit. So here
Edward Wilson-Ewing: you can see that a horizon has formed outside. So we've been out of horizon. We have an inner horizon. The star is collapsing, and then, if I play that forward, the bounce happens, and we see a shock that forms after the bounce. So we have a discontinuity in the outgoing. All expansion and the energy density
Edward Wilson-Ewing: of dust has become a very sharp pulse.
Edward Wilson-Ewing: Okay.
Edward Wilson-Ewing: So
Edward Wilson-Ewing: that's one example. We did a lot of examples, and we found
Edward Wilson-Ewing: very generally there's no singularity. It's replaced by a bounce. We find that a shock wave always forms at the latest at the Bam's time.
Edward Wilson-Ewing: We also found that bounce is stable, so there are some issues that show up when you construct a non singular black holes, especially in the vacuum case. You can. You may have some mass, inflation, stability, or instability in falling matter for white holes, and neither of these is an issue
Edward Wilson-Ewing: here. So everything is very stable. We also find a lifetime for the black hole from the formation of the outer horizon to its disappearance. When the shock wave exits which is proportional to the square of the Black Hole. Mass.
Edward Wilson-Ewing: Okay. So
Edward Wilson-Ewing: let me go back to the questions that I raised at the very beginning that the main points that we would like to address are the singularity and information loss, so as far as the singularity goes, in this specific model for black full collapse. It's very clear. There is no singularity. It's replaced by a non-singular bounce, and the formation of a shock.
Edward Wilson-Ewing: What about information? Loss
Edward Wilson-Ewing: well here this lifetime may be important, so we haven't
Edward Wilson-Ewing: done as much concerning information loss. But we can say a little bit.
Edward Wilson-Ewing: so we see that there's no singularity, and also there's no event. Horizon. There are apparent horizons, but these are only there for finite amount of time, and eventually go away.
Edward Wilson-Ewing: So this to me already suggests that there's no information loss, because.
Edward Wilson-Ewing: you know, at some point the current horizons are gone, and we should be able to recover the information, but we can actually make this a little bit more precise. So first.
the
Edward Wilson-Ewing: Lqg. Corrections at the horizon are extremely small, and are negligible. So hawking radiation will occur as usual. No changes there.
Edward Wilson-Ewing: but the predicted lifetime is much shorter than the page time.
Edward Wilson-Ewing: So what that means is that the entropy of the hawking radiation will always be much much smaller than the Black Hole entropy.
Edward Wilson-Ewing: So in principle, at least, there's no problem with purifying hawking radiation at a later time.
Edward Wilson-Ewing: So you have some a small amount of talking radiation which will presumably be entangled with matter or gravitational fields in the shock wave.
Edward Wilson-Ewing: and these degrees of freedom will be accessible to outside observers. Once the apparent verizon vanishes after the shock has gone beyond the short-shield radius.
Edward Wilson-Ewing: Now this is very much a sketch. There's a lot more work that's required to make this precise, and to show exactly how it may be possible to purify hawking radiation. But I think this gives us some hints and some directions for future research to really try and fill this gap.
Edward Wilson-Ewing: So
Edward Wilson-Ewing: I think i'm out of time. So i'll just put my
Edward Wilson-Ewing: summary up here. There's, of course, a lot of other steps that need to be done. Perhaps the main limitation of the work I presented is the gauges that are fixed before quantizing, and i'm very encouraged to see if there's been some work that may avoid imposing these gauges instead by
Edward Wilson-Ewing: cage, takes them with respect to matter, Field. So I think this is very complementary, and may be able to help, you know. Try some other complementary approaches, and see how similar the results are or not.
Edward Wilson-Ewing: But the main question that I want to emphasize here is that I think it's very important to include hawking radiation, and hopefully, explicitly show how we can recover information from Black Hole and purify what hawking the hockey mediation that was emitted by the Black Hole. So let me stop here and thank you for your attention.
Viqar Husain: Thanks to all the speakers we have. We're at 12. But let's have some
Viqar Husain: questions, so
please ask.
Viqar Husain: Are they? Look for hands? Here
LSU: I have a question.
Viqar Husain: please.
LSU: and up to be.
LSU: This is a a question for it.
LSU: and just a curiosity. And and and what is the size of the the radius of the of the of the mass collapsing the minimum right
LSU: it reaches during the collapse.
Edward Wilson-Ewing: so the minimum radius that it reaches. So let's do the simplest type where you have something which is approximately homogeneous
Edward Wilson-Ewing: in terms of dust.
Edward Wilson-Ewing: that then the minimum radius will be the cube root of the short shield radius times, the plank length squared.
Edward Wilson-Ewing: This is actually the radius. This is exactly the radius where the kretchman scalar, which is the plank scale.
Edward Wilson-Ewing: So it's not surprising.
LSU: Thank you.
Edward Wilson-Ewing: Yeah, you're welcome.
Abhay Vasant Ashtekar: Okay, I raise my hand, but I guess you don't see it.
Abhay Vasant Ashtekar: So I I got a couple of questions for LED.
Abhay Vasant Ashtekar: The thing is that the hawking radiation that you know talking did, and other people did, and which which was kind of supposed to be thermal, that is more or less
Abhay Vasant Ashtekar: at late times.
Abhay Vasant Ashtekar: and what you I mean, the in other words, the termality is at late times.
Abhay Vasant Ashtekar: So in your case, since
Abhay Vasant Ashtekar: your lifetime is much much shorter than hawking
Abhay Vasant Ashtekar: lifetime.
Abhay Vasant Ashtekar: You never reach that in late time.
Abhay Vasant Ashtekar: so it's not completely. It's not clear to me that
Abhay Vasant Ashtekar: the this information loss issue is is going to be much more complicated to analyze in your case.
Abhay Vasant Ashtekar: And but you know that people, I think Anderson, I think.
Abhay Vasant Ashtekar: has really talked about corrections to the hawking.
Abhay Vasant Ashtekar: the black body temperature at earlier time. So I think you should. It would be worth looking at that much, much more carefully
Abhay Vasant Ashtekar: you start really going to be.
Abhay Vasant Ashtekar: But also, I think the m squared. Is it that under
Abhay Vasant Ashtekar: some tension from observations. M squared is being too small
Abhay Vasant Ashtekar: for hawking radiation.
Edward Wilson-Ewing: I'm not so anything about it.
Edward Wilson-Ewing: Well, for for the first point I I agree. I I think this is something that I haven't really looked at any detail, and those corrections to formality could be very important.
Edward Wilson-Ewing: especially because, as you say, this is at relatively small time scales compared to what Hawking was was considering. So that's definitely something to
Edward Wilson-Ewing: to look at.
Edward Wilson-Ewing: as far as the time scale goes.
Edward Wilson-Ewing: Certainly M. Squared is
Edward Wilson-Ewing: larger than the lifetime of of the universe since the Big Bang era. Right so as far as that goes, there are no issues for solar mass, black holes, or anything that ligo is seeing.
Edward Wilson-Ewing: But I think that wasn't what you were worried about what?
Abhay Vasant Ashtekar: No, I I I I just meant that
Abhay Vasant Ashtekar: shouldn't we?
Abhay Vasant Ashtekar: No; but I think there are that sort of must black holes, but that the other way around, namely, that that
Abhay Vasant Ashtekar: black holes which are formed early on.
Abhay Vasant Ashtekar: you know. Like it's like it's a small. It's a it's a it's a it's a
Abhay Vasant Ashtekar: They should be exploding about now.
Abhay Vasant Ashtekar: but if, on the other hand, you know, they should, exploding a long, long time ago for you. And so I think that they they should add some signatures of that around.
Abhay Vasant Ashtekar: Yeah. So
Abhay Vasant Ashtekar: So so. So so that that all the
Edward Wilson-Ewing: right I'm: I'm: not a 100% sure about this. Because again, this is something I also haven't looked into in much detail. The first thing that I would say is that of course, this depends on the presence of primordial black holes. If there just aren't any, then, of course.
Abhay Vasant Ashtekar: correct so. But then you you you'll put really strong constraints, which will put a lot of people out of business, if you like, and then
Edward Wilson-Ewing: I I think we need to do more work before we can put in some constraints in that sense, because
Edward Wilson-Ewing: the so let me just explain. When I first did this I was, I initially thought that there may be some signature from when the shock wave comes out of the horizon.
Edward Wilson-Ewing: So let's say, there, there's some photons that are captured in the shock wave, the shockwave access to the rise, and then maybe these photons can now
Edward Wilson-Ewing: travel freely, and we can see them, and this may be some sort of energetic event that we observe from a distance.
Edward Wilson-Ewing: But then, if you look at it more closely. If the photons do start.
Edward Wilson-Ewing: you know.
Edward Wilson-Ewing: moving freely at that point.
Edward Wilson-Ewing: there's still a very strong gravitational potential, and they'll be very strongly red, shifted.
Edward Wilson-Ewing: And so at least that effect
Edward Wilson-Ewing: doesn't seem to be easily observable now. There could be others that could in the shock way much after the horizon.
Abhay Vasant Ashtekar: It can form
Abhay Vasant Ashtekar: it. It. It goes out.
Abhay Vasant Ashtekar: you know what. If so, that's where Red Shift might not be so hard, so high. There, isn't it.
Edward Wilson-Ewing: Well, the the that the shock wave is still carrying mass.
Edward Wilson-Ewing: So if if if let's say, the shock wave is just outside the horizon, let's say you know Schwarzschild plus some delta. Is that what happens? I I thought, that's real quick, and you, you know, can be very, very far away from them.
Edward Wilson-Ewing: Yeah. So so so I think the question is, if if let's say, there are photons that are traveling with the shock wave, At what point do the photons leave the shock wave.
Edward Wilson-Ewing: Do they leave it just when it access the horizon? Then the red shift will be very strong, but if they travel with the shock, they have a little bit longer before they leave it. Then the red shift could be smaller, and then there could be some observational effects. But but this is something I really have no idea about
Yeah.
Abhay Vasant Ashtekar: No one more question. Question. Okay.
Abhay Vasant Ashtekar: Go ahead.
Western: Can I interject just for a second it's a follow up from about this because of the case of the the phenomenology of an exploding like. So with lifetime. M. Square has been studied extensively by myself for alien Borrow and the students, so I don't so. Of course. Now I had this, considering the mechanism in which you have a shock wave, and I think the main difference with respect to what we have done before is the fact that you need a a white world.
Western: a horizon basically to in what we were doing to have all the the matter coming out, but I think that the the constraints that we put to the constraints they were in in those series of papers from the last year. So we're already answering the kind of questions that the By. Was trying to rise. So I think there could be a complementarity between this all the literature and what I is doing now.
Edward Wilson-Ewing: Yes, I think so, too.
Viqar Husain: Can we go to Yuri? I think he had his hand up. Eric, please.
Jerzy Lewandowski: Oh, thank you, I a I actually I have a some scattered and short questions to the E to the presentation. So there there was that in bookings. In the presentation there was that diagram
Jerzy Lewandowski: in which a. A. Is is some Ds 2 times s 2 space time is separated from
Jerzy Lewandowski: by some horizon, and
Jerzy Lewandowski: and so my question is, isn't it?
Jerzy Lewandowski: Hmm. Isn't. This a horizon extremal or on one side, and no external on the other side.
Muxin Han: No.
Muxin Han: no! The right from at the right, and it it looks just like classical
Muxin Han: classical Schwarzschild space time
Muxin Han: I see, so it's not. It's not the extreme All, even though it's not a spacetime inside. No, no, no, the yes, there, there's no there's no any quantum fact. Well, it's it's very. It's being extremely it's not quantum. It's also classical. It's just the different horizon.
Muxin Han: Yeah, the the horizon. Just look at it. Looks very much like.
Jerzy Lewandowski: yeah. But does it look the same on on, on, on on both sides.
Muxin Han: so it doesn't have the same geometry when we look at it from the Ds 2 times it's 2 side. No from just 2. You don't really see this right, because this Ts 2 is really but infinity
Muxin Han: is a scribe, and it's only a leave at a square plus.
Muxin Han: And I'm asymptotically infinite as future.
Jerzy Lewandowski: Okay. So what is in this region in this trapping trapping region? What what is it?
Jerzy Lewandowski: Is it all?
Abhay Vasant Ashtekar: It's a very complicated job it to which keeps oscillating and does all kinds of things. That's right.
Jerzy Lewandowski: I see. And now why? Why? Why the horizon? Why, this killing horizon is not the event horizon. So so what is what is
Muxin Han: right? It's just because it's it's there's no similarity, so it's. It's not a a standard. You know it's not not standard
Muxin Han: a black hole. Space Time is but but event. Event. Horizon is defined by future of of the of of sky. So if also has a space like component. So I saw light from the inside goes out to the space like component.
Abhay Vasant Ashtekar: But but then but the 1 point that mission sort of you. We discuss this in great detail, but what what you use of didn't play out with
Abhay Vasant Ashtekar: that? I think it is a little bit
Abhay Vasant Ashtekar: little bit imprecise to say that this space, like sky, is Ds 2 process 2, because it's
Abhay Vasant Ashtekar: so. It's really become so. It's not really a boundary. And so. The questions that you like is asking
Abhay Vasant Ashtekar: is, it is partially relevant because it's it's only
Abhay Vasant Ashtekar: it's. It's all very close to that sky. You can say that value says to cross it, I see. So this is asymptotically, and and 1 one more question about this quantum region. So
Jerzy Lewandowski: so you are so happy that you can extend the classical metric along this quantum vision. But but this is I I mean, what what is physically important? What is the stress energy tensor. So if you kind of calculate the Einstein tensor of this region, and think of this.
Jerzy Lewandowski: It tensor classically as as team, you know. What is it? How is it? Is it? Oh, it's, it's it's it's it's it's complicated. So we we what is the size? I would worry about the size more and even level than
Muxin Han: to side. Well, it's the size, the metric, you know, the the the entire space time Metric depend on some parameters, some free parameters, and the size of these space time is also is also a free parameter.
Muxin Han: Of course you can't shrink this size inside the to be. There are 2 horizons.
Muxin Han: and it's coming from your your space time. There are 2 horizons, so i'm the size of this B region cannot be inside these 2 horizons. It must be outside of it. So there is a lower bound basically distance between these 2 horizons.
Muxin Han: But I mean, there's no in principle. There's no upper bound.
Jerzy Lewandowski: And what is the curvature of the curvy? What is the curvature there?
Muxin Han: The curvature? I'm. A part of it will be plunk in, I mean, because the in the Verizon and your spacetime. The unit Verizon is has plunking curvature, so which means in between the altar and in the horizon. And there's there's already a a plank in
Muxin Han: regime, and then this regime extend to this B region
Muxin Han: A part of the B region. It's: it's it's a plank in conversion.
Viqar Husain: Okay, thank you. Okay, Good. Let's go to a a long in.
Viqar Husain: I think that's the next 10, though.
Erlangen: So hello, so so, so, so. So the point is like we can also use this the frequency matching model to study the vacuum case.
Erlangen: but from that from the from the presentation of this 3 panelists. So it seems like if they go to this vacuum case, so we will get some in
Erlangen: some different redoubt. So I want to ask those panelists. So what's what are their comments on this being consistency with each other, or what? As they created them to the other models.
Viqar Husain: So if I understand the question, you're asking the panelists to criticize each other. Is that right?
Erlangen: Yes, there is. There are all all the comments on this in consistency with each other.
Viqar Husain: Oh, okay, so maybe, can you briefly give those comments? We have a couple of at least one other person asking questions.
Okay. So for
Viqar Husain: yeah. But go first. Yeah.
psingh: I think like
psingh: I I think that is the most important question right now. I I I think all of these
psingh: 3 top show
psingh: 3 different angles in which you approach the problem.
and
psingh: I do not fully understand what is the complete picture starting from a dynamical collapse and what will be inside, how relevant will be the group quantization of the
psingh: course called Space Time at a later stage, or maybe it is going to give us many insights like this story is still unraveling.
psingh: So I would say like it is premature to
psingh: really answered that question. Now I I think we still need to understand
psingh: many things, even in the dynamical case what motion has done, and we are one season AI space time that was seen earlier for the Boimer vendors load. We learned many lessons
psingh: what LED is doing, is it's very encouraging. But there are issues of how we understand gauge, fixings, and so on.
psingh: So I think it will
psingh: not be. I I won't be wise to say, like, okay, this is the story, and this is the lesson for the dynamical picture. I think, like
psingh: the bridges. There are still many bridges to be made, and this is a very complicated
psingh: space-time.
psingh: whichever way you look at it, and I think
psingh: I don't know the final answer in this case. I'm: Sorry.
Viqar Husain: Okay, machine, and then add very briefly.
Muxin Han: So this is one of the reason why I I present tool stories. So so Firstly, this first story is about Covariance, right, and Covariance. We need to put some constraint on on the on the effective dynamics. Yeah, there are too many voices.
Muxin Han: and one of the constraint is probably General Covariance. And here we show that, at least for for these effective, that them it's the general covariance. Is it is satisfied. Yeah. And then the second story is that how about we don't use effective dynamics?
Muxin Han: Yeah. And we have we? We only consider something when we trust. And, for example, we we know a successful story about I to see, and and we know what
Muxin Han: for Black Hole, and we know, and we have some symmetry considerations. We won't have some feeling semi-free somewhere in the space time and then yeah, there is a this the B region that is mystery, and then we can look at what kind of metrics that we can put it in. Yeah, and it's it's different from
Muxin Han: It's mostly the physical considerations. Instead of computing effective equations for this, for this story. Yeah. And then we when if we
Muxin Han: then we look at this spacetime, If this spacetime is, then we can I mean using these physical considerations to to select a good, effective dynamics? That is my comment.
And
Edward Wilson-Ewing: no, I I think a lot of already been said I, I think i'll just
Edward Wilson-Ewing: essentially echo what both prom and mission have said, and maybe add that I think at this stage it's, you know. I think we're making progress in all of these directions.
Edward Wilson-Ewing: and it would be foolish to
Edward Wilson-Ewing: put all our eggs in one basket. So I think we need to keep on making progress in various directions, and each of these perspectives, I think, is complementary to the others.
Edward Wilson-Ewing: and
Edward Wilson-Ewing: ultimately, when once we figure it all out, I think we'll be taking ingredients from all of them. So I think all of these things need to be
Edward Wilson-Ewing: are are very valuable, but also none of them are yet fully complete.
Edward Wilson-Ewing: So
Viqar Husain: good thanks. And we have one more question: is that sufficient there?
Viqar Husain: Oh, yeah.
Viqar Husain: question.
Abhay Vasant Ashtekar: Can I just say this with 2 both things, small things. And answer to this question, please.
Abhay Vasant Ashtekar: Yeah. So one thing is that I think in the Aos model.
Abhay Vasant Ashtekar: but did not have enough time to talk about the exterior, but the metric is asymptotically flat, I mean, and and the idea of mass is well defined.
Abhay Vasant Ashtekar: But still, but I quickly mentioned that the curvature does not dk as fast as it normally does
Abhay Vasant Ashtekar: in the
Abhay Vasant Ashtekar: in, in, in in classical gr. For a syndetically flat spacetime, and I think that in the exterior reason the kind of things that, for example, machine is doing.
Abhay Vasant Ashtekar: bishing, and Hong Kong are doing in the
in the exterior
Abhay Vasant Ashtekar: for the vacuum case, that geometry and similar other geometries are all meadow and pull in, and that meaning have done in the exterior that geometry is probably better
Abhay Vasant Ashtekar: than the a way geometry that came up. It will be good to understand the relation between the 2
Abhay Vasant Ashtekar: in the interior region. On the other hand, I personally find that the
Abhay Vasant Ashtekar: the the the thing that machine talked about in the interior job it to there
Abhay Vasant Ashtekar: it's really not controlled, and we don't understand there are many aspects of physics there which I think are not completely understood when lots of detailed discussions about this. And so there i'm. Not so confident about this
yup
Abhay Vasant Ashtekar: whole bunch of bounces that occur, and all kinds of things that have occurred. Physical reason of that it's not completely. It's not at all clear to me.
Abhay Vasant Ashtekar: So the future asymptotically, the setup of
Abhay Vasant Ashtekar: up to some region inside the inside, the the the the first horizon. Everything is okay, but pushing and on. Go on do, but much later it doesn't seem to be very, very good. So there, I think one could take some lessons from some Aos model in the the pure vacuum case.
Abhay Vasant Ashtekar: So I think that kind of complimentary, this sense.
Viqar Husain: Okay, thanks, bye, we have one more question, vessel, please.
Veso: Hey? Can you hear me.
Viqar Husain: Yes.
Veso: thank you. To all the our panelists and the moderator. It was very interesting.
Veso: I need few qualifications from each of the speakers.
Veso: For the first one. I I was wondering if you can just briefly remind me
Veso: what is the Cnc. Bar, B+B bar? I assume P.
Veso: C. And Tb. Are actually the momentum. But i'm not sure.
Veso: That's my first question to
Veso: on my 3
Veso: and the second question for the second speaker.
Veso: I wanna make sure I understand. So the idea that
Veso: in the me
Veso: gravity, when you up the desk
Veso: effectively, you are removing the
practically, you're fixing the gauge.
Veso: If I understood correctly.
Veso: and for the third one i'm not sure if I understand
Veso: by 12 that
Veso: basically the shock waves can out from the event horizon. Is that really possible? From physical point of view. If you have a black hole.
Veso: so they These are my 3 questions, and I was appreciative.
Veso: The speakers can quickly give me some qualifications.
psingh: So if I understand the question correctly, you are asking what the Pb. And PC. Parts right? So they are the triads.
psingh: and so PC. Is essentially
psingh: the, and sits in front of the angular part of the metric, and it's equal to 4 M's. Care
psingh: and the ratio of Pb. And PC. Comes in what will be the Gxx part? It doesn't have a
Oh.
psingh: as nice relationship, or something like Pb. Scale by PC.
psingh: What about the C. And B. C and B are the momentas, or you can think of Cn, C and B are the 2 of the components of the
psingh: they Are they? So the poison. Right? They are the conjugate variables. B. And Pv. And C. And PC. Are the conjugate variables.
Veso: But physically it is not anything related to speed of light or anything like that.
psingh: No, no, I'm sorry. Like the C. Has nothing to do with speed of light. That's just the connection component.
psingh: I'm: Sorry.
Viqar Husain: Yeah. We Shane? Briefly.
Muxin Han: Yes, yeah. The answer is, you are. You are right. You are right. And so so the the Hamiltonian is based on the foliation of this internal time. 5. That's why I say, we say, this is a physical Hamiltonian. This is true, Hamiltonia instead of Hamiltonian constraint.
Muxin Han: And so
Edward Wilson-Ewing: yeah, so so that's right. So the shock really corresponds to discontinuity in the gravitational field. So you can ask, how is the shock moving with respect to the metric on the outside, and with respect to the metric on the inside.
Edward Wilson-Ewing: and it turns out that the shock moves in a time like way with respect to the metric inside, but in the space like way with respect to the metric outside. So that is it inside the horizon. So you can think of this as being some sort of effective violation of the dominant energy condition which allows you to move in a space like way and eventually reach the outer horizon.
Veso: Okay, but effectively, you cannot observe it, because there is a horizon between the 2 regions.
Edward Wilson-Ewing: That's right. Yeah, at least outside of
Veso: Yeah, thanks.
Edward Wilson-Ewing: You're welcome.
Viqar Husain: Okay. I don't see any other hands. Does anyone want to make any other comments?
Viqar Husain: I'm just going to scan here? I don't see anything. So
Viqar Husain: all right. Thank you to all the speakers and participants
Viqar Husain: Very interesting discussion.
Viqar Husain: and I think we can sign off.
Viqar Husain: Do you have any other questions? You can just contact the speakers correctly.
Viqar Husain: Thanks.
Muxin Han: thanks, bye, bye, Thank you.