WEBVTT 1 00:00:02.670 --> 00:00:07.630 Jorge Pullin: Okay. So our speaker today is Stefan Weigel, who will speak about effective Ltb models. 2 00:00:09.120 --> 00:00:17.239 Stefan Weigl: Thank you very much for the introduction. And first of all. I would like to thank the organizers very much for inviting me to give this talk here. 3 00:00:17.520 --> 00:00:29.110 Stefan Weigl: As already said, I am going to talk about effective Ltp models, and you can already find 2 associate papers to this talk on Archive, and they will be published soon. 4 00:00:29.240 --> 00:00:39.200 Stefan Weigl: The my collaborators in this project were Christina Giesel, Hong, Guang, Leo, Eric Ruddett, and Paramp Singh. 5 00:00:40.010 --> 00:00:44.560 Stefan Weigl: So let me start with a brief introduction to the topic. 6 00:00:44.600 --> 00:00:53.420 Stefan Weigl: So the overall question, which is, of course, a monumental task is, how do quantum gravity effects influence leg holes? 7 00:00:53.660 --> 00:00:56.810 Stefan Weigl: And this is 8 00:00:56.860 --> 00:01:17.709 Stefan Weigl: and a a topic through many quantum gravity communities. And here I tried to list a few people who were working on this from our community, and this list is, of course, far from conclusive. So I already want to apologize in advance if I forgot here some persons 9 00:01:18.630 --> 00:01:26.659 Stefan Weigl: to be more concrete. one class of models so called, eternal black hole models. 10 00:01:26.890 --> 00:01:42.620 Stefan Weigl: and these are models which try to already which start from an already formed black hole and try to to include now quantum corrections motivated from the quantum cosmology. 11 00:01:42.620 --> 00:02:04.739 Stefan Weigl: and this is possible due to the isom isometries into setup. For example, in the interior we will have a Kantowski sucks space time, and therefore we one can use some resize from look quantum cosmology in order to do this, and I want to refer at this point to 2 recent reviews on this subject. 12 00:02:05.400 --> 00:02:19.440 Stefan Weigl: Here, however, we are, yeah in into interested in another perspective. Especially, we want to see how this dynamical formation process is is 13 00:02:19.770 --> 00:02:28.409 Stefan Weigl: is happening. So we want to see what happens in a gravitational collapse with some quantum gravity effects 14 00:02:28.570 --> 00:02:48.609 Stefan Weigl: the typical setup. To to reduce the the complexity of this question is to only and consider spherical symmetric models. And further, as matter, we will restrict ourselves to dust. So this is a perfect fluid, with no pressure. 15 00:02:49.010 --> 00:02:50.819 Stefan Weigl: and in classical tr. 16 00:02:50.830 --> 00:02:59.910 Stefan Weigl: If on classical classical general relativity, the solution of the Einstein equation is given by the so called le Metre Tolmann, Bondiemont as space times. 17 00:03:01.010 --> 00:03:22.380 Stefan Weigl: And further, we will do this in in this in in our approach in an effective description. So this means, we will work in a classical model which includes some correction functions. And these correction functions have the role of of implementing the quantum gravity corrections 18 00:03:22.400 --> 00:03:24.409 Stefan Weigl: add a quantum gravity effects 19 00:03:25.620 --> 00:03:37.600 Stefan Weigl: in the literature most models described the Oppenheimer Snyder scenario. So this means that here one has a homogeneous dust ball 20 00:03:37.630 --> 00:03:40.980 Stefan Weigl: embedded in a vacuum. And 21 00:03:41.480 --> 00:04:00.889 Stefan Weigl: this simplified setup allows, for example, certain for example, to use classical junction conditions in order to glue this interior space time, which is usually modeled by some Friedman, or, better to say, modified Friedman equations to some exterior 22 00:04:00.890 --> 00:04:14.320 Stefan Weigl: space time, which when us which one is usually imposing certain symmetry restriction on. So we have symmetry. And also we consider aesthetic space times. 23 00:04:14.870 --> 00:04:25.090 Stefan Weigl: And one interesting question that arose in this context is in these dust. Collapsed models is whether there is a discontinuity in the gravitational feet forming 24 00:04:25.160 --> 00:04:49.979 Stefan Weigl: after the bounce. So before the bounce, more or less, all models are coherent, but after the bounce they they they diverge a bit and related to this question, is also, the fact how these equations of motion look, and if we can have a decoupled equations of motion since coordinates similar, like in the classical case. 25 00:04:51.060 --> 00:05:07.520 Stefan Weigl: And this is where we want to try to to contribute to this discussion, and our approach is to construct effective Ltb models from an underlying effective spherical symmetric model. As a one plus one feeds theory 26 00:05:07.760 --> 00:05:11.070 Stefan Weigl: under certain assumptions. I will come to this later. 27 00:05:11.310 --> 00:05:15.159 Stefan Weigl: and this means we are especially interested. 28 00:05:15.810 --> 00:05:23.340 Stefan Weigl: Consider a general answer for these effective models, and we will not only restrict ourselves to 29 00:05:23.530 --> 00:05:45.940 Stefan Weigl: to a certain polymerization schemes like, for example, scheme which can be also motivated from a reduced quantization. But here, more more. Our perspective is to see which kind of restrictions on this general effective model. Such a dynamical and implementation of an Ltp. Sector constraints. 30 00:05:46.810 --> 00:06:08.969 Stefan Weigl: And one of the advantages of this approach is then, that since we are working in in Ltb, we can basically consider arbitrary dust mask profiles. So this means as a special case. This includes vacuum or polymerized vacuum and open habits, nider scenario, but also real smooth in homogeneous dust. Profiles, too. 31 00:06:09.940 --> 00:06:24.780 Stefan Weigl: And one advantage of knowing this spherical symmetric model is that, for example, there's no area gauge set on this radio coordinate. Yet. So in distance we have. There are some coordinate transformations. 32 00:06:24.930 --> 00:06:26.160 Stefan Weigl: possible. 33 00:06:26.810 --> 00:06:40.890 Stefan Weigl: And with that I want to show you the plan of the talk. So first of all, I am going to talk about classical LTB. And space times in the class and economical framework with connection variables. 34 00:06:41.130 --> 00:06:55.709 Stefan Weigl: Then we will. turn our focus to constructing effective Atp models. And we will do this by analyzing the dynamical stability of a so-called adb condition under the effective dynamics. 35 00:06:56.500 --> 00:07:15.509 Stefan Weigl: Then I will consider a concrete model which we will. which we will construct from from from from adapting to improved acc dynast solution in the marginally bound case. 36 00:07:15.730 --> 00:07:24.709 Stefan Weigl: and also see that extended mimetic gravity can give an underlying, coherent lagrangian of this canonical framework. 37 00:07:25.790 --> 00:07:32.940 Stefan Weigl: Then we will discuss further the polymerize vacuum solution and compare to other models in the literature. 38 00:07:33.140 --> 00:07:36.759 Stefan Weigl: And finally, I will conclude with a summary and an outlook. 39 00:07:37.780 --> 00:07:42.010 Stefan Weigl: Okay, so let us start now with classical LTB. Models. 40 00:07:42.550 --> 00:08:05.400 Stefan Weigl: So we work as usual in real bear variables where the Hamiltonian has the standard form. It's a combination of constraints, since we are in spherical symmetry, and we only have one nontrivial spatial direction, which means we only have one different morphism, constraint, and also only one Gauss constraint, and this is the scalar constraint. 41 00:08:05.860 --> 00:08:32.059 Stefan Weigl: We can impose the spherical symmetry on the triad and the connection components, and this will restrict the freedom of this components to only 3. And we can see that the spherical symmetric metric can be written in terms of these trial components, for example, in terms of EX and E. Phi, which is related to 2 components. And here we can see 42 00:08:32.360 --> 00:08:46.520 Stefan Weigl: they are not. they are not completely determined by by this this to try components only up to a rotation of thereof. And this we can fix when we when we use the Gauss constraint. 43 00:08:46.520 --> 00:09:06.139 Stefan Weigl: So fixing that goes constraint into setup, we are then in a phase, space which has only to them 2 degrees of freedom anymore. And this and as conjugated pairs, we can choose. Then this symmetry restricted triad components, and the components of the extinction curvatures. 44 00:09:06.300 --> 00:09:16.940 Stefan Weigl: Additionally, we will consider we will add dust to our gravitational system, and we call it T, and because we will use it as as a dust, time, reference, feed 45 00:09:18.220 --> 00:09:45.090 Stefan Weigl: so in this. Try it. Variables. We can now write the Ltb solution, which is now only a function of ex and the dynamical equation which has to hold. And here we have 2 free functions. So first of all, we have the Ltp function, which is this curly E, and it's only a variable on X has no phase, space, dependence. And this curly F, which is 46 00:09:45.560 --> 00:09:57.670 Stefan Weigl: basically a measure of the of the of the dust. Mass distribution. And this LTB. Function is a measure of the total energy of a shell at radio coordinate X 47 00:09:57.970 --> 00:10:06.479 Stefan Weigl: and discussed this effort by the total gravitation, gravitation, a mass inside of a shell at radius X 48 00:10:07.380 --> 00:10:26.990 Stefan Weigl: and also some, some, some, some some definition on over in the case that this Curly E is 0. We will call this the marginally bound case, and if it's non 0, this is the non marginally bound case, the marginally bound case is very closely related also to the vacuum case. 49 00:10:28.590 --> 00:10:32.770 Stefan Weigl: So now, comparing this, the Ltp solution 50 00:10:33.060 --> 00:10:34.409 Stefan Weigl: to the 51 00:10:34.440 --> 00:10:52.759 Stefan Weigl: the general form of the spherical symmetric metric we see we have to do a certain identification. First of all, the lapse function has to be one, and the shift vectors vanishing. And further, there has to hold a relation between the 2 triad components, and this condition we will call the Ltp condition. 52 00:10:53.700 --> 00:11:06.349 Stefan Weigl: and it turns out that we can reduce the spherical symmetric. metric! the spherical symmetric system to this l tb. Sector by implementing 2 gauge fixings. 53 00:11:06.350 --> 00:11:24.250 Stefan Weigl: So first of all, we can gauge, fix the the Hamiltonian constraint with respect to the dust, time, gauge. So this will set, then the the labs function to one, and further we can gauge. Fix the different constraint with respect to this ltp condition. 54 00:11:24.820 --> 00:11:28.989 AAipad2022: So after gauge fixing what are the degrees of freedom left? Is the 55 00:11:29.340 --> 00:11:32.649 AAipad2022: F and N. Energy density free now or 56 00:11:32.910 --> 00:11:43.799 Stefan Weigl: and no, no, there, there are no degrees of freedom, and we have 2 canonical variables left, which is will be one component of of these extensive curvature and one of the triads. 57 00:11:44.000 --> 00:11:51.610 Stefan Weigl: But what about the matching? The matter is is reduced as a because of the dust time. Gauge. 58 00:11:51.840 --> 00:11:52.880 AAipad2022: Okay, thank you. 59 00:11:54.320 --> 00:11:55.649 Stefan Weigl: Thank you for the question. 60 00:11:55.690 --> 00:12:16.070 Stefan Weigl: One interesting fact here is, one has to be careful a little bit with this gauge fixing when working in the marginally bound case, because here, when we already implemented this task, time, gauge turns out that the Ltb condition is not anymore conjugated to the, to the dipom constraint. 61 00:12:16.070 --> 00:12:37.760 Stefan Weigl: So this means, here they actually are first class, and in this sense we have to add the atp condition as another first class constraint to the system. And this will mean that in this setup no physical degrees of freedom are left anymore. But we will see this is consistent in the Hamiltonian framework, because here also the Hamiltonian will only be a boundary term. 62 00:12:39.080 --> 00:12:45.589 Stefan Weigl: All right. So let's turn our focus to the Fa. To effective Ltb models. 63 00:12:45.670 --> 00:12:52.499 Stefan Weigl: So as motivated from the fact, what's happening in the in the classical system? 64 00:12:52.500 --> 00:13:18.100 Stefan Weigl: We will directly go into a partially gauge fix effective system where we implement already the dust time gauge fixing because we are mostly interested whether we can make this Ltp reduction. So this means we will consider a Hamiltonian where we now have a gravitational contribution to the scalar constraint. And this data means that it's an effective one or polymerized one. 65 00:13:18.230 --> 00:13:19.110 Stefan Weigl: and 66 00:13:19.300 --> 00:13:24.810 Stefan Weigl: then we have the one diffomorphism constraint which takes in these variables this form. 67 00:13:25.050 --> 00:13:35.810 Stefan Weigl: Here's already one of the assumptions we make. We will not, consider an effective different constraint, but work with the classical one. 68 00:13:36.770 --> 00:13:54.090 Stefan Weigl: and the form of this gravitation! Contribution of the scalar. Constraint is given by this by this term here. So we have introduced here 3 polymerization functions H. One and H. 2 and an F function. 69 00:13:54.100 --> 00:14:01.169 Stefan Weigl: The 2 H functions they encode inverse. Try it inverse, try it corrections, and have a classical limit of one. 70 00:14:01.300 --> 00:14:23.389 Stefan Weigl: And this this generalized autonomy corrections. Because of how we introduce it has a classic element of 0. And this not only in encodes Holonomy corrections because it's it's allowed to depend on this extrinsic curvature components, but also encodes right corrections due to this ex component. 71 00:14:23.640 --> 00:14:28.639 Stefan Weigl: And in this way we define our general answers of effective models. 72 00:14:29.130 --> 00:14:34.500 Stefan Weigl: So are are these constraints, I mean, in which you polymerize one, but not the other. 73 00:14:34.880 --> 00:14:37.289 AAipad2022: is the yes. What is the constraint? Algebra 74 00:14:37.780 --> 00:14:54.039 Stefan Weigl: really come to this? So first of all. Here. One can see that because we don't want to change the density weight of the scalar constraint. This will mean that once on bracket, it has still the normal form between the diffum constraint and the scalar constraint. 75 00:14:54.060 --> 00:15:18.610 Stefan Weigl: So this is just a normal relation. And of course the X with the axis has also exactly the the same relation as in the classical case. The interesting question is now whether still the basically the bracket of C delta with theta closes. And in in this Hamiltonian context this means, if C. Delta is a conserved quantity in the different sector. 76 00:15:19.040 --> 00:15:33.570 Stefan Weigl: and it turns out if you want to have this already? This imposes severe. Restrictions on the polymerization functions, namely, no polymerization of Kx will be allowed anymore. 77 00:15:33.680 --> 00:16:01.399 Stefan Weigl: And further, there has to hold a relation between the inverse triad corrections and the Holonomy corrections in this way. And this is not only a restriction because of these derivatives, but also the left hand side is only a function on EX. So in these Holonomy corrections, now they only they are only allowed to depend on the K. Phi. X. 20 curvature. They also have to be in this combination only a function of the triad. 78 00:16:01.500 --> 00:16:15.790 Stefan Weigl: So here to to to show how we define this F. One F. 2 functions. It means that F, one is encoding the Kyle extension curvature and Phi direction squared term. And this is the linear K 5 term. 79 00:16:16.940 --> 00:16:26.490 Stefan Weigl: And one note is because we and I wouldn't call this constraint algebra here, since we are already in a partially gauge fixed Hamiltonian 80 00:16:26.510 --> 00:16:51.389 Stefan Weigl: and and the constrained algebra should be analyzed in the fully gauge unfixed system. So this means it depends also what kind of Meta you couple to the system in general. But it turns out this is very similar to what also Alloa Alonso Bada, considered when they couple dust to the Meta and analyze the closure of the constrained algebra. This relation here. 81 00:16:52.890 --> 00:16:58.940 Stefan Weigl: So now we want to come to the effective Ldp sector. 82 00:16:59.220 --> 00:17:16.340 Stefan Weigl: and this means we will have, we will introduce, first of all, an effective atp condition. So to remind you, the classical one has this form where we have the relation of the trial components. Just to this atp function E, and 83 00:17:16.690 --> 00:17:25.930 Stefan Weigl: now we also allow the phase, space functions to appear, and also arbitrary derivatives of thereof. 84 00:17:26.440 --> 00:17:46.210 Stefan Weigl: and what we will do now is to see when we can. When we make this Ltp condition dynamically stable. And this was already. Investigated in a smaller in in an early context. By by 85 00:17:46.300 --> 00:17:56.929 Stefan Weigl: and here we will extend and and generalize these results. We will call such dynamical, stable adp conditions compatible. 86 00:17:57.370 --> 00:18:26.719 Stefan Weigl: And our strategy to do this will be that we that we are going to work on the equations of motions. So this means the the dynamic stability is then equivalent to the questions for which effective ltp conditions due to 4 equations of motions reduced to only 2 in the sector where we have a vanishing shift. Vector the different constraint and the Ldp condition vanishing. 87 00:18:26.900 --> 00:18:33.529 Stefan Weigl: and the 2 variables one usually chooses, and which have the simplest equations is K, phi, and EX. 88 00:18:34.540 --> 00:19:02.469 Stefan Weigl: So first result in this investigation is already that the compatible atp conditions are not allow, are not allowed to actually depend on this arbitrary derivatives. But first of all, there's a contribution which which is basically done on margin Deli case. So there's a dependence on this Ltp function. Only K fine ex dependencies allowed in this G Delta function. 89 00:19:02.520 --> 00:19:13.530 Stefan Weigl: and only if we only considered a marginally bound case. Also there is an while this Kx Twitter Tilde dependents allowed. 90 00:19:14.510 --> 00:19:19.529 Stefan Weigl: So this is basically their contribution. This corresponds to the marginally bound case. 91 00:19:20.280 --> 00:19:37.290 Stefan Weigl: And now, you want to see? Which kind of restrictions do these these compatible idb conditions come impose on the polymerization functions which we have in our scalar constraint, effective scalar constraint. 92 00:19:37.820 --> 00:19:46.600 Stefan Weigl: First of all, the first observation is that there is an additional constraint when an KX. Polymerization is involved, and 93 00:19:46.730 --> 00:19:53.540 Stefan Weigl: when we are in an unmarkingly bound case. This means that actually also no Kx polymerization is allowed. 94 00:19:54.860 --> 00:20:00.630 Stefan Weigl: However, if we, if we in a much in a marginally bound case. 95 00:20:00.640 --> 00:20:19.640 Stefan Weigl: we have to basically restrict ourselves to to an Ltp condition which has only these 2 dependencies to also get the same result. So the marginally bound case one has a little bit more wiggle room, but when restricting the form of this Ltp condition, one gets the same result as in a non marginally bound case. 96 00:20:21.070 --> 00:20:31.439 Stefan Weigl: So secondly, when we separate this add function dependence on the to data. So this means we figured out this 97 00:20:31.450 --> 00:20:34.790 Stefan Weigl: this Ldp function in a non-marginally bound case. 98 00:20:34.840 --> 00:20:45.240 Stefan Weigl: then the compatible atp condition is only aligned to to only allow to depend on this invest on this trial component. And further. 99 00:20:45.240 --> 00:21:05.129 Stefan Weigl: there has to be a a relation fulfilled between this the atp condition and the Holonomy corrections. And if you remember from the slide before this term looks very similar to the conservation of the Delta case, and so, naturally, there's a close connection, then, between 100 00:21:05.420 --> 00:21:17.029 Stefan Weigl: having a compatible Ltp condition and a conservation of C. Delta. And this to also have the conservation of C. Delta. We can write in this context. And this relation. 101 00:21:18.710 --> 00:21:32.349 Stefan Weigl: Yeah, we can now also see if we want to go to the classic if you want to and have a classic condition in the effective framework. So this means that there's no trial dependence in this G twiddle. 102 00:21:32.350 --> 00:21:48.790 Stefan Weigl: This means that actually the we have this. This thing has to be one. So there is a is A. This relation on the Holonomy correction has to hold alone from the compatibility of and of the classical Ltp condition in this effective framework. 103 00:21:48.820 --> 00:22:00.080 Stefan Weigl: And further, if we want to have additionally the conservation of the data also, there is another condition on the inverse riot components. 104 00:22:00.830 --> 00:22:18.010 Stefan Weigl: One observation, for example, is here that we cannot only have in this, in this sector, the and non-trivial non-trivial. H. One correction infest right correction. Since then, this relation is violated. 105 00:22:19.420 --> 00:22:27.470 Stefan Weigl: Okay, so now let us concern. Let us go discuss the dynamics of these models. 106 00:22:27.590 --> 00:22:42.059 Stefan Weigl: So considering a system with compatible Adb conditions, we can very generally show that these equations of motions are actually decoupled if we look at at a 107 00:22:42.090 --> 00:22:49.369 Stefan Weigl: at also at the case, that the C. Delta is conserved. So this effective scalar constraint is a conserved quantity. 108 00:22:49.410 --> 00:23:03.020 Stefan Weigl: then the dynamics of these models in the Addb sector have the following form. So this looks a bit complicated. But the important thing is basically that no radial derivatives are appearing here on the right hand side. 109 00:23:03.730 --> 00:23:12.299 Stefan Weigl: And this condition, these equations of motions are applicable in the marginally and also in the non marginally bound case. 110 00:23:12.870 --> 00:23:26.220 Stefan Weigl: and they are not marginally bound case. We can get to the same result when we implement the gauge. Fixing with respect to this Ld effective Ltp condition and compute the 111 00:23:26.230 --> 00:23:29.790 Stefan Weigl: that the rug bracket associated to it. 112 00:23:30.920 --> 00:23:42.060 Stefan Weigl: And this result, for example, shows that the assumption of decoupled chess, which was which was assumed in some dust collapse models can be true. 113 00:23:42.910 --> 00:24:04.300 Stefan Weigl: and another effect. And and again, I want to say that in this Hamiltonian framework, so the solution is parametrized, first of all by this Ltb. Function, E. Which is not a phase-based function. It's just a radial function, basically a free parameter, and also the conserved quantity mass of a shell. 114 00:24:05.880 --> 00:24:21.749 Stefan Weigl: And this is especially intriguing. Now, this decoupled sector, since now we, we can build a concrete model. From from improved accuracy, dynamics. So and a general strategy to do this is basically 115 00:24:22.490 --> 00:24:28.429 Stefan Weigl: we can choose an an effective accuracy model as a starting point. 116 00:24:28.550 --> 00:24:40.750 Stefan Weigl: and use foregone corollary or the foregone green box to identify. The the form of the effective Fergusymatic model and the Ltp condition. So 117 00:24:41.050 --> 00:24:44.639 Stefan Weigl: I can read this basically off. And in this way 118 00:24:45.270 --> 00:24:57.380 Stefan Weigl: we can can first of all get the underlying spherical symmetric model that has no area gauge implemented yet. So we have this coordinate transformation, freedom on the radio coordinate. 119 00:24:57.400 --> 00:25:11.840 Stefan Weigl: And secondly, we have a dynamical stable reduction to the Ltb sector. With this effective Ltp condition so, and here dynamically stable with respect to the effective dynamics. 120 00:25:12.060 --> 00:25:20.969 Stefan Weigl: And third, these equations of motions are decoupled and and exactly coincide with the chosen Acc model. 121 00:25:22.110 --> 00:25:38.680 Stefan Weigl: and sometimes, which will be the case, and the model will. consider! Next one can even then relate this effective Ferguson model, the Sis effective Fergus symmetric model to an underlying cover and Lagrangian. 122 00:25:38.740 --> 00:25:59.510 Stefan Weigl: and in our model this will be extended magnetic gravity in the co-moving gauge, and in this sense we can then regain the coordinate transformation in the temporal coordinate. Since they then correspond to redefining the dependence on the on the the time dependence of this magnetic field which serves as a clock. 123 00:26:00.440 --> 00:26:04.040 Stefan Weigl: We will see this like later. 124 00:26:05.050 --> 00:26:33.809 Stefan Weigl: So we want to start now with the following, equations of motions. So in in B+B coordinates, we can write. This improved accuracy! Dynamics in in this way, where V is now related as the power of 3 half of ex, and b is k phi, divided by square root of EX, and this alpha parameter is related to the barbarian parameter and minimize area gap and accuracy. 125 00:26:34.890 --> 00:26:36.440 Stefan Weigl: And 126 00:26:37.270 --> 00:26:48.500 Stefan Weigl: Comparing this with the general form of the equations of motions. We can then deduce that and this spherical symmetric model is the underlying 127 00:26:48.520 --> 00:27:00.990 Stefan Weigl: model, which is already found by Tipuvala. Here, in this paper. due to the effect that we don't have any inverse try corrections. For example. 128 00:27:01.020 --> 00:27:04.340 Stefan Weigl: the compatible Ldp condition is exactly the classical one. 129 00:27:04.710 --> 00:27:10.489 Stefan Weigl: and this also means that we are, and in this C. Delta conserved sector. 130 00:27:12.300 --> 00:27:41.859 Stefan Weigl: and we can rewrite these equations of motions which we have under foreground page in terms of modified Friedmann equations, and in terms of this capital R. Coordinate, then the then, the metric takes this form here, where the the case, when now the radial derivative of R. Vanishes. This metric is degenerate, and this is a so-called shell crossing. 131 00:27:42.610 --> 00:27:51.010 Stefan Weigl: and sometimes the shell crossings can also give rise to singularities. It depends on how the mass function is chosen. 132 00:27:51.240 --> 00:28:04.390 Stefan Weigl: and we and we will come back to this matter. And due to this modified Friedman equations, we can for and, for example, see that we can also have bounces in these models for certain critical energy densities. 133 00:28:05.550 --> 00:28:15.689 AAipad2022: For the, for the upcoming talk. Just take over this model that was joining 134 00:28:15.750 --> 00:28:20.260 AAipad2022: 2,012 by Tibetwala. So what have you? What I mean? 135 00:28:20.540 --> 00:28:24.310 AAipad2022: What it? What more have you learned now? Like 136 00:28:24.350 --> 00:28:26.910 AAipad2022: more extended your work. 137 00:28:26.980 --> 00:28:28.520 AAipad2022: which is much more general. 138 00:28:29.140 --> 00:28:31.270 AAipad2022: If, in fact, we're going to get 139 00:28:31.830 --> 00:28:35.410 AAipad2022: the underlying spherical models symmetric model to be the same as before. 140 00:28:36.500 --> 00:28:41.670 AAipad2022: Why, I mean? Why, the the extra work you did. So what did we learn? New? What is a new thing that we learned? 141 00:28:42.270 --> 00:29:11.379 Stefan Weigl: So so basically, what we learned is in in in this setup. We can. So so, Tipper, while I did not consider any Ldb sector or something like this, and this is exactly the connection that we show, so that basically we can implement an effective adb reduction. Starting from this effective model and have decoupled equations of motions which exactly are the form of this improved accuracy dynamics. 142 00:29:11.730 --> 00:29:26.510 Stefan Weigl: This is basically our input. What tperwala came to this very symmetric? Lagrangian, if I'm correct by considering different polymerizations and and analyzing whether the constrained algebra closes. 143 00:29:26.670 --> 00:29:33.049 Stefan Weigl: and and this is also similar related in our language to the effect that the C. Tilde is conserved. 144 00:29:33.500 --> 00:29:44.610 Stefan Weigl: So in our. And so what is different, or what is our new endpoint is is basically that we that we show this relate this effective Ltp relation and the equations of motions there. 145 00:29:50.450 --> 00:29:52.330 Stefan Weigl: Okay. 146 00:29:52.900 --> 00:30:06.599 Stefan Weigl: Well, then, let me continue here. For the for the upcoming talk. We will now re restrict our analysis to this marginally bound case. So this means we will set this energy function to 0. 147 00:30:06.900 --> 00:30:17.650 Stefan Weigl: And then we can find the analytic analytic solution to these decoupled equations of motion, and this is given exactly by this expression here. 148 00:30:17.820 --> 00:30:38.599 Stefan Weigl: Where this Beta is an arbitrary function of X, and this curly F is again the master distribution we can choose, and if we have if we consider homogeneous dust, which means that this is just. X to the power of 3 and some constant, and the solution was already derived in these 2 papers here. 149 00:30:39.080 --> 00:30:41.960 Stefan Weigl: Setting this constant. 150 00:30:42.130 --> 00:30:44.290 Stefan Weigl: then we are in the vacuum solution. 151 00:30:44.890 --> 00:30:59.259 Stefan Weigl: And we can see, for example, due to this square here, that we have a type symmetry, and also since here we can choose without loss of generality. This Peter, to be just X. This metric is, of course, clearly stationary 152 00:31:00.060 --> 00:31:01.690 Stefan Weigl: and 153 00:31:01.850 --> 00:31:15.250 Stefan Weigl: from studying. Now, the solution for mass profiles of this vacuum, or Oppenheimer Snyder collapse? We. We can see that we actually will not have any shake crossing singularities. 154 00:31:15.320 --> 00:31:16.999 Stefan Weigl: but in the 155 00:31:17.090 --> 00:31:27.860 Stefan Weigl: general, in homogeneous case this is not true. And here I want to refer to one very new paper, which was just uploaded last week. 156 00:31:29.260 --> 00:31:43.420 Stefan Weigl: and we can then also investigate the formation of horizons by computing the expansion parameters related to the solutions. And what we will see is 157 00:31:43.420 --> 00:32:04.410 Stefan Weigl: that depending on the demands which depends on X has to be above a certain lower mass bound, and this is the same mass bound as derived by these 3 papers, and this will mean, in particular, that, for example, for for low, for small x there will be no horizons forming. 158 00:32:05.390 --> 00:32:11.560 Stefan Weigl: we will see this at the very end of the talk, also in a picture in A, on Home, in the, in homogeneous case. 159 00:32:13.360 --> 00:32:19.489 Stefan Weigl: So let me now talk about this underlying, covariant Lagrangian. 160 00:32:19.970 --> 00:32:40.790 Stefan Weigl: So because we, and as spherical symmetric models this is only a Tel. 2D. Action. But what what can be shown is that this primary Hamiltonian that we consider so in our effective spherical, symmetric model. This can also be derived from this Lagrangian. In the co-moving gauge. 161 00:32:40.860 --> 00:32:48.990 Stefan Weigl: So this ex. This extended memetic theory is an it's a conformal extension of Einstein gravity. 162 00:32:49.010 --> 00:33:11.590 Stefan Weigl: And we have 3 parts basically, in this action. First of all a curvature part, and secondly, here a mimatic, a mimetic condition on the mimic, the mimetic condition, or the mimetic fit phi, and a potential which encodes higher derivative coupling. Between the the mimetic field and the geometry in x and y 163 00:33:12.550 --> 00:33:14.100 Stefan Weigl: and 164 00:33:14.680 --> 00:33:36.659 Stefan Weigl: One thing to note here is that we not couple this with the typical determinant of the metric, but with respect to the triad such that we have a parity odd function, and this will then allow for us that, for example, one of the triad components in this setup, the if I is allowed to change the signature. 165 00:33:36.850 --> 00:33:40.649 Stefan Weigl: and this is necessary to to to 166 00:33:40.950 --> 00:33:44.880 Stefan Weigl: correctly reproduce the accuracy. Dynamics in this model 167 00:33:45.730 --> 00:33:57.080 Stefan Weigl: and this mimic model naturally defines a foliation, because the smooth memetic field due to the mimic relation 168 00:33:57.220 --> 00:34:25.420 Stefan Weigl: basically can can foliate the that that space time into space like slices where the file is constant. And this means that without loss of generality we can fix. We can say we can reduce to the case where the magnetic field is only allowed to depend on this time calling that in our case, because we go to the into the school moving gauge. This will be just T. 169 00:34:26.210 --> 00:34:33.930 Stefan Weigl: And, as I said, the higher derivative coupling in X and Y can be seen in the definition, a 170 00:34:34.290 --> 00:34:56.269 Stefan Weigl: yeah of these quantities where we have. The, with respect to this. With respect to the 2D metric, and here and this coupling, and in the co-moving gauge, actually, these quantities, X and y directly relate to the extrinsic curvature of on a on such a Phi even equal constant slice. 171 00:34:56.880 --> 00:35:10.630 Stefan Weigl: and the difference now to classically, gr can be seen. For example, when we take the variation of this Lagrangian and and and derived upon all of the Einstein equations. 172 00:35:10.810 --> 00:35:11.860 Stefan Weigl: because. 173 00:35:12.160 --> 00:35:34.060 Stefan Weigl: first of all, there is a non rotational dust field. Appearing source from the mimetic field. And additionally due to this mimic potential, we have an additional stress energy. Tensor appearing due to this higher derivative coupling. And and we can basically add this now to the classical Einstein tensor 174 00:35:34.310 --> 00:35:44.000 Stefan Weigl: have an effective Einstein tensor in this way, which now includes also quantum gravity effects or effects from this polymerization. 175 00:35:44.560 --> 00:35:47.859 Stefan Weigl: I think it's bit confusing for the audience. And 176 00:35:48.140 --> 00:35:53.380 AAipad2022: so this is a completely new chapter. This has nothing to do with what it's talked about before. Is that correct? 177 00:35:54.350 --> 00:36:20.419 Stefan Weigl: So this this relation one can do only for certain effective models for the mimic, for the effective models I showed you here. This is possible, but for general effective models one cannot do this relation to the Lagrange to display. But your model has no scalar field. Your model does not. So what is the relation between what was done before? And now what you're doing now? 178 00:36:21.660 --> 00:36:35.529 Stefan Weigl: So so yeah. The. So this is not a new reside. But we have. You had no scale of fee. And now, suddenly, there is a scale of feed. There are various other things happening. 179 00:36:35.580 --> 00:36:44.500 AAipad2022: so it would be helpful for us to understand the relation between what you spoke up to now, and what you are now talking about, that would be very good for us to understand. 180 00:36:45.340 --> 00:36:58.709 Stefan Weigl: Okay, so so wh. What is good with this link to this Lagrangian is 2 things. So, first of all, we have now a possibility to get a Lagrantian to our Hamiltonian. 181 00:36:59.040 --> 00:37:14.489 Stefan Weigl: and and therefore Einstein equations. And secondly, we we regain, in a certain sense, this temporal transformations, but which are then these redefinitions of the time, dependence of this mimic field. 182 00:37:15.220 --> 00:37:40.489 Stefan Weigl: And secondly, or thirdly, we can. And this, yeah, the effective system. So this polymerization contributions can be sourced by this mimic field. That's the thing. So so in this sense, one can interpret these polymers effects as coming from exotic meta, contributions to 183 00:37:40.540 --> 00:37:43.549 Stefan Weigl: to to to to our system. 184 00:37:44.980 --> 00:38:05.289 AAipad2022: You also said one stage, that if I change the signature I don't understand the meaning of that word. If I just a function, what does it mean if I change the signature so so when we now look at the dynamics, we will see that actually in vacuum at the bounce, for example. This, if I try. It will change the signature 185 00:38:05.490 --> 00:38:08.979 AAipad2022: signature in sign or signage sign 186 00:38:09.030 --> 00:38:10.669 AAipad2022: sign. Okay? Okay? Yeah. 187 00:38:11.330 --> 00:38:18.770 Stefan Weigl: So it will come, go from a positive value than to a negative values. Mostly. That's what I mean. 188 00:38:19.680 --> 00:38:20.490 Hongguang Liu: Okay? 189 00:38:33.470 --> 00:38:49.700 Hongguang Liu: And if you look at the if you look back the right hand side also, that's the after. I didn't think that's why it's related to the previous and license which we have a desk copy, and then everything can 190 00:38:49.870 --> 00:38:52.279 Hongguang Liu: rewritten the RGB. Covenant. 191 00:38:52.450 --> 00:38:55.960 Hongguang Liu: I think we have a. 192 00:38:59.620 --> 00:39:01.789 AAipad2022: So you are saying that this is 193 00:39:03.260 --> 00:39:07.380 AAipad2022: I mean, you can think of the Phi as it does. And I didn't understand the statement that you just made. 194 00:39:07.600 --> 00:39:09.440 Hongguang Liu: This is Rick. 195 00:39:09.880 --> 00:39:18.410 Hongguang Liu: Yes, yes, you can. You have seen you have seen everything at the desk at the desk. 196 00:39:18.980 --> 00:39:20.029 AAipad2022: Okay, thank you. 197 00:39:21.670 --> 00:39:27.360 AAipad2022: But dust. But previously does not null gravest right in the 198 00:39:27.590 --> 00:39:29.830 AAipad2022: in the previous transparencies. It was 199 00:39:29.920 --> 00:39:45.140 Stefan Weigl: so. So is this a completely different system. No, it was also notation. It does. But this, if this mimic feed is not only the mimic dust sourcing, but also the polymerization contributions to the Hamiltonian. So it has 2 200 00:39:46.090 --> 00:39:47.519 2 chops. Basically. 201 00:39:48.760 --> 00:39:57.960 Stefan Weigl: it's our reference field, but also sourcing our if our polymerization effects so quantum gravity effects in this setup as an effective model 202 00:39:58.360 --> 00:40:10.180 Hongguang Liu: and also previous analysts. Also. No version, no rotational. That's because we don't. we don't contribution to the 203 00:40:13.690 --> 00:40:18.050 Hongguang Liu: we only use to depend dependent time. 204 00:40:22.500 --> 00:40:29.199 Stefan Weigl: okay, I hope that? Answers that question. 205 00:40:29.420 --> 00:40:37.170 Stefan Weigl: So then let me continue here with a specializing on the polymerized vacuum case. 206 00:40:37.270 --> 00:40:51.539 Stefan Weigl: So now we want to and restrict ourselves to the vacuum, which means that this dust mass distribution function will be set to constant. This is already done, and just to papers, too. 207 00:40:51.650 --> 00:41:05.630 Stefan Weigl: and then the solution takes the following, from where now we can introduce this zet, which is just X minus t, and we can see that this metric is clearly stationary cost is the only dependence of the metric on this R function, as we saw. 208 00:41:06.320 --> 00:41:07.200 Stefan Weigl: And 209 00:41:07.390 --> 00:41:34.029 Stefan Weigl: now one just has to be careful a little bit, since this vacuum does not mean that we have a flat geometry. So so first of all, vacuum means that this dust contribution we saw in the Einstein equation, the energy density, lambda is 0, but the curvature is not vanishing, and this can be seen, for example, here. That even at the bounce, where it has the biggest value. It's still bounded. 210 00:41:34.760 --> 00:41:51.159 Stefan Weigl: But it's never vanishing. And this is due to this higher derivative coupling of the mimetic field in terms of this additional stress energy tensor appearing in the Einstein equations, and we would interpret them as a quantum gravity effects. 211 00:41:51.720 --> 00:42:03.009 Stefan Weigl: And, as I said already it's everything boundless. So this means also we don't have any share. Crossing singularity appearing in this vacuum case even at the bounds, which is the most quantum region. 212 00:42:03.730 --> 00:42:21.839 Stefan Weigl: And here, what I also already mentioned on the first slide. We will have to signature. Change any Phi since due to the relation due to the Adb condition, we have a relation between E 5 and the radio derivative of X 213 00:42:21.850 --> 00:42:31.800 Stefan Weigl: and plugging in our solution, we can see that the bounce which is at set equal 0 we have here different signatures and the derivative. 214 00:42:32.040 --> 00:42:51.499 Stefan Weigl: And this this is consistent with the fact that also here the metric is degenerate. So if I go trans. Going from a positive to a negative through 0, so at that bounce, it's actually degenerate. But one can check that, for example, also that geodesics can pass through this the bounce. 215 00:42:52.490 --> 00:42:59.230 Stefan Weigl: And so it's more a coordinate effect, and not a real physical singularity in this sense. 216 00:42:59.520 --> 00:43:03.589 Stefan Weigl: So it's not a, it's not a coordinate effect, right? I mean, if you just vision right then. 217 00:43:04.040 --> 00:43:07.919 AAipad2022: whether metric is digital. It or not is not a coordinate effect. Right? I mean. 218 00:43:08.400 --> 00:43:10.770 Stefan Weigl: yeah. 219 00:43:10.800 --> 00:43:11.870 AAipad2022: So okay. 220 00:43:12.010 --> 00:43:15.939 Stefan Weigl: it's it's not a similarity, but it is still a 221 00:43:16.420 --> 00:43:21.330 AAipad2022: I mean, it's not a metric at that point, if you like, because if it's degenerate by definition, it's not a metric. Okay? 222 00:43:21.680 --> 00:43:30.509 AAipad2022: But the dynamics is digit. The dynamics is deterministic. Nonetheless. 223 00:43:30.820 --> 00:43:32.000 Stefan Weigl: Thank you. 224 00:43:32.680 --> 00:43:51.969 Stefan Weigl: So what we now can what we now want to do is to to relate our solution via coordinate transformations now to other models in the literature, and also, for example, discussing the the appearance of shocks in this context. And 225 00:43:52.390 --> 00:43:58.629 Stefan Weigl: first, let let us focus on the poly polymerized vacuum case, and here we can 226 00:43:58.630 --> 00:44:28.339 Stefan Weigl: transform from our Ltp coordinates Tx to to watch it like coordinates Tau and R, where the metric takes the the. This typical form as a function of this AR, which is then now not only the classical result, but also has some quantum corrections proportional here to this Ipa square, and this is, exactly the same solution which was also derived in these 3 papers. For example. 227 00:44:29.380 --> 00:44:55.960 Stefan Weigl: however, one thing to note here, this coordinate transformation is is only well defined when when r of set is monotonic, and we saw that R is a a function of of set square. So this means that actually, before the bounds are after by the bounds, we can do this, but not at the bounds. And in this sense, the space times can have different global structure. 228 00:44:57.250 --> 00:44:58.150 Stefan Weigl: And 229 00:44:58.630 --> 00:45:19.920 Stefan Weigl: now, concerning the area gauge. Here, basically 1. One works in Gtp coordinates. And to to get to this coordinates, one gauge fixes the different morphism constraint. When we are in this very symmetric system. With respect to this area gauge fixing and not with respect to the Ltp gauge fixing. 230 00:45:20.130 --> 00:45:35.579 Stefan Weigl: And then the solution of the Si shift vector is given by by this sign of the of K. 5. And we can see that we can exactly reproduce the model of Hussein Kelly, Santa Cruz, and with new wing and 22. 231 00:45:36.300 --> 00:45:48.849 Stefan Weigl: And then, after gauge, fixing the different morphism, constraint, we will, which one can then reduce to the LTB. Sector. However, in this context, the equations of motions are not decoupled. 232 00:45:50.070 --> 00:46:10.289 Stefan Weigl: and to relate our solution directly to this choice of coordinates, we can for example, we can make a corner change to this Gtps and and and what we can see here is that then the shift vector, is just a tempered derivative of our solution are. 233 00:46:10.580 --> 00:46:12.650 Stefan Weigl: And this means that 234 00:46:12.740 --> 00:46:29.109 Stefan Weigl: our solution impose naturally, also a sign change on on of the shift vector at the bounds which is not observed when one directly works in in the ready. In this our coordinates 235 00:46:29.110 --> 00:46:44.040 Stefan Weigl: in the vacuum case. And this. Roughly speaking, also, is the is the is the reason for for discontinuities appearing so for for the appearance of shocks in the Oppenheimer, Snyder collapse scenario. 236 00:46:45.130 --> 00:46:53.430 Stefan Weigl: So to to see this global structures. In in more detail. One can, for example, consider 237 00:46:53.620 --> 00:47:14.760 Stefan Weigl: X equal constant space times in these other coordinates. And let us focus here and on this first picture on this first figure. So in this, watch it like coordinates, Tau and R plotting this X equal constant at your desk. We see when we check in which directions. 238 00:47:14.760 --> 00:47:36.229 Stefan Weigl: increasing. TS, that's the sign vector the sign arrow, and the Red arrow is pointing towards increasing X direction and and now, comparing these 2 arrows before the bounce to after the bounce we will see from the perspective of Ltp coordinates for T. And X. This orientation is changed. 239 00:47:37.190 --> 00:47:40.170 Stefan Weigl: and further, even more severely. 240 00:47:40.200 --> 00:47:46.589 Stefan Weigl: since this X. Equal constant geodesics are also the word lines of our clock field. Phi. 241 00:47:46.730 --> 00:48:00.359 Stefan Weigl: we see. They intersect after the bounce with word lines of of a greater X. And this means that we have to to introduce discontinuities in our clock field. 242 00:48:00.360 --> 00:48:19.040 Stefan Weigl: which, very similar to the observation in the paper of and this violates the smoothness of our so in this sense this tower coordinates are not a good description of the of the dynamics. 243 00:48:19.890 --> 00:48:40.380 Stefan Weigl: and what one has to do in order to to get the same global structure in R coordinates as as in the in the Tx coordinates is to glue, basically a different patch of r coordinates after the bounce with a different orientation, which is exactly described by Johannes Mitch in this paper. 244 00:48:41.710 --> 00:48:43.179 Stefan Weigl: and 245 00:48:43.290 --> 00:49:03.900 Stefan Weigl: technically, since we on the under level of solutions. There is a 2 to one correspondence between the set or X coordinates and the R. Coordinates we can identify 2 different geodesics. When concerning their coordinate transformations, and 246 00:49:04.420 --> 00:49:28.470 Stefan Weigl: actually when when we want to see if in our setup also, shock solutions are allowed. We can introduce effective junction conditions which are derived from this effective Einstein equations in our case, and see if there are a non-trivial surface matter. Contributions appearing. 247 00:49:28.470 --> 00:49:39.870 Stefan Weigl: and due to this 2 to one correspondence, not only we can have the usual gluing, but also a gluing where we change to the orange line, which is exactly the minus set 248 00:49:39.870 --> 00:49:47.790 Stefan Weigl: geodesic at the bounce. And what we see I don't want to go there into details is that 249 00:49:48.100 --> 00:50:05.709 Stefan Weigl: basically in in both ways of gluing, no surface and stress energy tensors appearing. So this means without violating the smoothness of our clock field of our mimic feed, and in this way we we don't see any any shocks appearing. 250 00:50:06.030 --> 00:50:17.500 Stefan Weigl: And here, on the right hand side I just want to show the conformal diagram of our space time. So this is very like the Reissner north stream. One. 251 00:50:17.510 --> 00:50:30.499 Stefan Weigl: The only difference is that due to our Orient, change our orientation change at a bounce. We have to glue of another tower of these 252 00:50:30.760 --> 00:50:39.569 Stefan Weigl: These Penrose diagrams which are identified at at this minima radius and direction, and in blue. One can see, for example, one of 253 00:50:39.590 --> 00:50:41.500 discussed lines 254 00:50:41.570 --> 00:50:51.110 Stefan Weigl: going through this through the bounce, and then ending up in another universe with apparently universe with a different orientation than the original one. 255 00:50:51.210 --> 00:50:55.139 Stefan Weigl: And these are in both directions here 256 00:50:55.560 --> 00:50:57.810 Stefan Weigl: infinitely extended. 257 00:50:58.660 --> 00:51:04.880 Stefan Weigl: So now I want to only very shortly speak about the inhomogeneous case. 258 00:51:04.950 --> 00:51:17.159 Stefan Weigl: since here one can see that now a single shake crossing singularities up here. Also observed, in in this in this paper. 259 00:51:17.580 --> 00:51:40.099 Stefan Weigl: so as we saw for very small X values there can be no horizons. Which I hear this white dashed lines, but when we have a bounce there is also shake crossing, appearing, and what the shade crossing singularity is doing. And it's it's basically protecting or separating the space time into 2 260 00:51:40.130 --> 00:51:42.830 different patches with different orientations. 261 00:51:43.590 --> 00:51:58.170 Stefan Weigl: So here the annotation is switched. With respect to this one. It looks like these singularities are weak singularities, because also to designing can pass through. But this needs further investigation, and this work in progress. 262 00:51:58.940 --> 00:52:04.300 Stefan Weigl: And with that I want to come to a summary. So first of all, 263 00:52:04.650 --> 00:52:20.760 Stefan Weigl: I showed that our framework allows the construction of effective Ltp models with Holonomy and inverse right corrections under certain assumptions. So, for example, that no polymerization of the different morphism constraint is, is 264 00:52:20.800 --> 00:52:22.260 Stefan Weigl: is implemented. 265 00:52:22.360 --> 00:52:39.569 Stefan Weigl: Then we can see that certain effective, effective Ltp models have decoupled dynamics, and this then allows us to to take an Aq. C model as a starting point and construct from their efficioratic model for an inhomogeneous dust collapse. 266 00:52:40.420 --> 00:52:55.220 Stefan Weigl: and sometimes as in in this concrete model, we can use the underlying limited model to to to provide a Lagrangian formulation and also have regain all the coordinate transformations. 267 00:52:55.690 --> 00:53:12.999 Stefan Weigl: And in future. One interesting question would be, for example, to study further phenomenological properties like whole evaporation, using these effective Einstein equations from our underlying covariant framework. 268 00:53:13.260 --> 00:53:14.230 Stefan Weigl: And 269 00:53:14.440 --> 00:53:27.869 Stefan Weigl: additionally, another perspective would be to extend the A the analysis to accuracy models which has an asymmetric bounce. And this is work in progress right now. 270 00:53:28.450 --> 00:53:32.840 Stefan Weigl: And lastly, another perspective would be to 271 00:53:32.860 --> 00:53:52.250 Stefan Weigl: look to study more closely the different polymerized we can have in this class of effective theories. And for example, see if there might be a pick of like a Crm in this context, this is also work in progress. And 272 00:53:52.260 --> 00:53:56.769 Stefan Weigl: with this I want to close the talk and thank you for your attention 273 00:54:02.970 --> 00:54:05.840 Jorge Pullin: questions. I believe. 274 00:54:06.570 --> 00:54:11.039 AAipad2022: Yeah, II have a couple of questions. One. If you can go back to your slide. 17, just for a second. 275 00:54:11.780 --> 00:54:13.790 Stefan Weigl: Now. 276 00:54:14.110 --> 00:54:14.780 AAipad2022: Beck. 277 00:54:14.920 --> 00:54:20.280 AAipad2022: so I mean II there, there is some confusion in the community, and I would like to 278 00:54:20.730 --> 00:54:22.360 AAipad2022: take this occasion to 279 00:54:22.520 --> 00:54:26.819 AAipad2022: understand the the current our our current understanding. 280 00:54:27.230 --> 00:54:33.830 AAipad2022: I mean the the paper that you referred to. I think if I remember correctly. 281 00:54:34.120 --> 00:54:37.910 AAipad2022: They said that it's really the pandemic coordinates 282 00:54:38.440 --> 00:54:47.509 AAipad2022: which was use a Parliament, or that was wrong in the sense that that gave rise to some coordinate singularity, whereas physically, nothing is happening. 283 00:54:47.610 --> 00:54:50.460 AAipad2022: and and certain 284 00:54:51.130 --> 00:54:53.250 AAipad2022: effects that were seen before. 285 00:54:53.290 --> 00:55:06.679 AAipad2022: By, for example, by the the group in Canada, where, where? Just coordinate artifacts, and that, in fact, there was no physical problem at all. 286 00:55:07.020 --> 00:55:12.759 AAipad2022: And you are saying something now from the point of view of the mimetic field, Phi. 287 00:55:13.430 --> 00:55:16.699 AAipad2022: and because they did not have mimetic fields at all. 288 00:55:17.170 --> 00:55:25.339 AAipad2022: But but is a statement that what you are saying in terms of mimitic field is exactly the same as what was in Taniya saying. 289 00:55:25.720 --> 00:55:27.269 AAipad2022: or is there something different? 290 00:55:27.980 --> 00:55:33.740 Stefan Weigl: Partly, yes. So so 1 one argument is, 291 00:55:33.820 --> 00:55:42.830 Stefan Weigl: because of the due to the different properties we post to our clock field, which, for example, is a discontinuity or a smoothness. 292 00:55:42.900 --> 00:56:06.229 Stefan Weigl: For example, this does not allow shocks, but so so in the sense, what what in this paper was done is that the show? If you use different coordinates, you can. You can have no singularities, and therefore no shocks have to be implemented. However, from our inspective we can extend this this work in the in the sense that 293 00:56:06.250 --> 00:56:12.219 Stefan Weigl: because we have now a a full model in the sense we don't use junction conditions. 294 00:56:12.450 --> 00:56:28.779 Stefan Weigl: we can actually, in the Oppenheimer Snyder case. See from our, for in this a Ltp coordinates there is no singularity appearing, and even if you try to use junction conditions at the boundary of the star. 295 00:56:28.790 --> 00:56:57.329 Stefan Weigl: there is still no surface energy, density. And this and this is in our case, the the analog on to shock solutions. We have to do it like this because we don't have coupled differential equations. So it doesn't make sense here to go into speak solutions. But we can go to the Einstein equations and and look for distribution, a solution which is a exactly function pond. Now in our effective framework. 296 00:56:57.510 --> 00:57:22.000 Stefan Weigl: So in this sense, we, we extend this a bit. Because of our underlying Lagrangian formulation, and say, even when one tries to, because of this, 2 to one correspondence of T and X, or Atp coordinates to this Gtp coordinates, we can. We can consider a different gluing than the normal one, which and and even then we don't find shocks. 297 00:57:22.390 --> 00:57:31.009 AAipad2022: Okay, good. And the second thing was about again. This the I would like to understand better understand the relation with limiting gravity 298 00:57:31.180 --> 00:57:38.970 AAipad2022: from what you know, what the other. So the way you presented it was also kind of starting with 299 00:57:39.310 --> 00:57:52.039 AAipad2022: certain answers for for this desk collapse right for the Ltb model, and the I mean, you know that you don't change it if you want some constraint, but you probably by the totally constraint, and so on, so forth. 300 00:57:52.440 --> 00:58:04.889 AAipad2022: And then you arrive at some point. And then you said, basically, Yeah, but these are the equations. But these equations could also be derived from the pneumatic gravity. If you make some identifications with the scalar field as being 301 00:58:04.970 --> 00:58:18.199 AAipad2022: dust, erotic, irrotational dust field. That's all right. But could I not also take the point of view that the fundamental theory just limited. And I just write it down the questions. 302 00:58:18.230 --> 00:58:25.189 AAipad2022: And then what you're done is a sector of that theory. Is that a consistent thing, or am I missing something? If I took that point of view? 303 00:58:26.350 --> 00:58:49.719 Stefan Weigl: yes, but but, as I already tried to say before, this cannot be done for arbitrary, effective models. So so only for certain polymerization functions. If you want, we can tune this and mimic potential here such that it can source this. This quantity effects. 304 00:58:49.750 --> 00:58:58.390 Stefan Weigl: But you're completely right in in this subsector. One can see this as the underlying theory in a certain co-moving gauge. 305 00:58:58.540 --> 00:59:10.550 Stefan Weigl: Yeah, which is only a might restriction on the geometry. As I pointed out here with this natural 48 point of view, that what you wrote down Lagrangian is a theory that you look at. 306 00:59:10.670 --> 00:59:20.009 AAipad2022: and it is not obvious that this theory contains, you know, TV. But but, on the other hand, you show that it does contain it to be. And this is explicit proof of that. 307 00:59:20.060 --> 00:59:24.059 AAipad2022: That's I mean it does it? It seems like many, many other components, right? 308 00:59:24.090 --> 00:59:28.670 AAipad2022: Ltbs, and so, okay, thank you. Thank you. That's that's very clarifying. 309 00:59:29.060 --> 00:59:41.470 AAipad2022: Yeah, I ask this question because you know, we've got experts. Hong Kong Wong was talking about before, and I think Vicar is an audience so that people may want to contribute so that we can connect various approaches. 310 00:59:42.020 --> 00:59:43.329 AAipad2022: Thank you very much 311 00:59:44.500 --> 00:59:45.410 Jorge Pullin: regard. 312 00:59:46.010 --> 00:59:58.480 Viqar Husain: Oh, yes, I just wanted to ask a clarifying question. I think the results, for, as I understand the results of no shocks both in of Hazini at all's paper, and your work relates only 313 00:59:58.630 --> 01:00:16.650 Viqar Husain: to the Oppenheimer Snyder model. Is that correct? And not to be in homogeneous profiles? Oh, yes, yes, yes, for sure. II only wanted to say this gluing is only possible in the Oppenheimer Snyder case, of course. Yes, so II just wanted to clarify that in general, when you do have 314 01:00:16.680 --> 01:00:33.459 Viqar Husain: the. And this was our recent work. With Ed and Francesco. In our recent work. What we show is that the decoupled odes that you obtain are actually the characteristic equations of a nonlinear Pde. 315 01:00:33.490 --> 01:00:40.580 Viqar Husain: And so when you actually look at that nonlinear, PDE. And look at the most general initial data profiles. 316 01:00:40.600 --> 01:00:45.070 Viqar Husain: Then shock waves are an essential part of that. 317 01:00:45.450 --> 01:00:50.380 Viqar Husain: So that's just a comment and encouragement for you the rest of you to look at that paper 318 01:00:50.660 --> 01:00:58.139 AAipad2022: right? But for for you're talking about yes, the the full. It's basically a one plus one field theory. 319 01:00:58.180 --> 01:01:11.540 Viqar Husain: and the one plus one field theory can be looked at in more than one way one way to look at it is to consider the equations that we just saw, which were the decoupled point odes. 320 01:01:11.590 --> 01:01:19.520 Viqar Husain: And what we show in that paper is that these decoupled point odes are exactly the characteristic equations of a nonlinear. PDE. 321 01:01:20.650 --> 01:01:25.830 Viqar Husain: And the of the nonlinear Pd can include shock waves. 322 01:01:28.770 --> 01:01:40.700 Viqar Husain: Yeah, I'm really happy that you know. P. Various people spoke up, because then one can get a global picture. So I think there are multiple aspects aspects of this, and I think it's as as you 323 01:01:40.730 --> 01:01:46.830 Viqar Husain: I mentioned Stefan. I think it's very important to study the inhomogeneous cases from multiple angles as well. 324 01:01:47.180 --> 01:01:57.119 Viqar Husain: yeah, for sure. Because the the Openheimer Snyder collapse, in a sense, is, of course, only an idealized picture. Yeah, it's basically a quantum mechanics model. Right? So. 325 01:01:57.730 --> 01:01:58.470 Stefan Weigl: yeah. 326 01:02:01.760 --> 01:02:02.690 Jorge Pullin: Ed. 327 01:02:06.490 --> 01:02:11.710 Edward Wilson-Ewing: yeah, thank you. The car actually said most of what I wanted to say. But let me just add one quick point. 328 01:02:11.820 --> 01:02:19.900 Edward Wilson-Ewing: If we look at the Oppenheimer Snyder case, what happens is that we find that these characteristic curves that require us discussing that they cross. 329 01:02:20.030 --> 01:02:26.320 Edward Wilson-Ewing: And so in Openheimer Snyder. It's a little confusing, because this could signal either hey! 330 01:02:26.580 --> 01:02:29.860 Edward Wilson-Ewing: Formation of a shock or the fact that the coordinates fail. 331 01:02:29.960 --> 01:02:33.860 Edward Wilson-Ewing: and it's not obvious a priori, which one is the case. 332 01:02:33.940 --> 01:02:52.910 Edward Wilson-Ewing: and this is what was pointed out by in these other papers. And also it's Stefan has been presenting here. But if you look at more general cases. So if you allow for in homogeneity and homogeneous profiles, for example, including profiles that are very, very close to Openheimer Snyder. Then you get a shell crossing singularity. And then it's clear 333 01:02:53.150 --> 01:02:56.450 Edward Wilson-Ewing: because of this singularity. What it's saying is that actually, these 334 01:02:56.480 --> 01:03:02.779 Edward Wilson-Ewing: these characteristic curves crossing is physical is not a Coronadic artifact, and at that point you should really be looking for shocks. 335 01:03:03.300 --> 01:03:05.000 Edward Wilson-Ewing: So let me stop there. 336 01:03:05.340 --> 01:03:09.179 AAipad2022: Yeah. But I don't understand why you say the open Amish side. The case is, 337 01:03:09.580 --> 01:03:13.249 AAipad2022: there's ambiguity, I mean, you know, if, in fact, there existed 338 01:03:13.460 --> 01:03:22.249 AAipad2022: I mean, it is a bit like saying that there's ambiguity in the case of the Schwarzschild horizon. If there is singularity, not because it's some coordinate, there is, and some other coordinates there isn't. 339 01:03:22.280 --> 01:03:29.160 AAipad2022: And the whole point is that if there is one coordinate system in which everything is regular, then there is no singularity. 340 01:03:29.200 --> 01:03:34.700 AAipad2022: So I so II fully appreciate what you said just now, but you know, moojing this case that I fully appreciate. 341 01:03:34.950 --> 01:03:42.800 AAipad2022: But I don't see why there is any room for ambiguity in the open. I'm Ashinder case, and I would really like to understand that because I may be missing something here. 342 01:03:44.080 --> 01:03:50.659 Edward Wilson-Ewing: well, I would. I would just say that you can take the inhomogeneous case 343 01:03:51.080 --> 01:03:55.429 Edward Wilson-Ewing: and take a profile which is close to Oppenheimer Snyder, and you can take the limit. 344 01:03:55.900 --> 01:04:16.970 Edward Wilson-Ewing: And even when it's arbitrarily close. There'll still be a shock. Cross. Sorry a shell crossing singularity that'll form. So in that case, if you view it as a limiting process, then you may expect there to be a shock to there too. But if if you take it separately, then then I agree that there exist these extensions without any singularities there. There's no question about that. So I mean, it's a bit like saying that 345 01:04:17.040 --> 01:04:24.129 AAipad2022: if I looked at Short Shield as a limiting case of pricing. Then there is also always a inner horizon. 346 01:04:24.580 --> 01:04:34.140 AAipad2022: And it's true. So so same thing here for open it is another one, I mean, if you like, if it's like for the basis or something. 347 01:04:34.280 --> 01:04:36.329 AAipad2022: it's it's a special. 348 01:04:36.450 --> 01:04:39.900 AAipad2022: III completely maybe more accessible. 349 01:04:40.140 --> 01:04:44.969 AAipad2022: may maybe we should just say, this is a non typical case 350 01:04:47.730 --> 01:04:48.780 Jorge Pullin: on one. 351 01:04:49.470 --> 01:05:12.340 Hongguang Liu: Yeah. So that's the further, because we have a general solution. And then we can see that the 352 01:05:12.370 --> 01:05:22.140 Hongguang Liu: probably weekly. That's why, every time 353 01:05:22.620 --> 01:05:29.140 Hongguang Liu: you'll see the tricks and the the classical video. So we go to the shop solution. Okay, cool. 354 01:05:32.540 --> 01:05:34.880 Hongguang Liu: we can, we can have these kinds of decisions. 355 01:05:35.270 --> 01:05:46.770 Hongguang Liu: And and also 356 01:05:47.060 --> 01:05:50.510 Hongguang Liu: back to the whole 357 01:05:50.540 --> 01:06:00.290 Hongguang Liu: Edward side. And then. 358 01:06:12.230 --> 01:06:26.129 Viqar Husain: okay, we go. I just wanted to add one more comment in. Even in a classical Ltb collapse with no quantum corrections of any kind. There is initial data that leads to a shock wave on the infall 359 01:06:27.240 --> 01:06:33.210 Viqar Husain: for certain sets of initial data, and that's a little known fact. But it already exists in the literature. 360 01:06:34.240 --> 01:06:42.929 Hongguang Liu: Yes, yes. Why. 361 01:06:44.110 --> 01:06:46.040 the compensate moving treachery. 362 01:06:46.200 --> 01:06:48.569 Hongguang Liu: And we see that with red line battery. 363 01:06:49.100 --> 01:06:51.449 So why hold the red line? Why on the 364 01:07:06.450 --> 01:07:08.100 Hongguang Liu: produced by classical 365 01:07:09.100 --> 01:07:15.680 Hongguang Liu: classical? 366 01:07:16.130 --> 01:07:17.479 It's another 367 01:07:19.110 --> 01:07:20.400 Hongguang Liu: of the graphic possible. 368 01:07:25.300 --> 01:07:27.860 Jorge Pullin: Hmm. Any other questions 369 01:07:34.920 --> 01:07:37.249 Jorge Pullin: we have noticed. Thank the speaker again.