WEBVTT

1
00:00:05.100 --> 00:00:17.719
Kristina Giesel: Yeah, welcome to today's international quantum gravity Seminar. It's a pleasure, yeah, to have the opportunity to share these symposium on non-singular black holes. Today.

2
00:00:18.070 --> 00:00:32.029
Kristina Giesel: It was a suggestion from the Organizing Committee of the International Loop quantum Gravity seminar to do one seminar in this kind of format. And in this symposium. We will have 3 different speakers today.

3
00:00:32.608 --> 00:00:44.100
Kristina Giesel: They all have in common that they are in their final year of their Phd. And they also have in common that they did some recent work on black holes, non-singular black holes.

4
00:00:44.300 --> 00:00:58.350
Kristina Giesel: and the 3 speakers will be Francesco Fassini from the University of New Brunswick, and he will talk about the stellar collapse and shell crossing singularities in effective Lqg models.

5
00:00:58.470 --> 00:01:13.069
Kristina Giesel: So he will generalize the classical Oppenheimer Snyder collapse. Yeah, in 2 ways. On the one hand, he uses Aqg. Inspired effective models, and, on the other hand, he will also introduce a perfect fluid with pressure.

6
00:01:13.480 --> 00:01:30.880
Kristina Giesel: Then the second speaker will be Michel Bubula from the University of Worceloft. He will also modify the Oppenheimer Snyder collapse in a way that he will modify the vacuum solution and consider a non-singular Hayward black hole solution.

7
00:01:31.440 --> 00:01:45.759
Kristina Giesel: and the 3rd speaker will be Yunas neuser from the Fiu Erlangen Numberg, and he has recent work on Black hole perturbations with back reaction, that he will talk in the last talk of the symposium.

8
00:01:46.020 --> 00:02:03.810
Kristina Giesel: So the format that this symposium will be made of is that each speaker will give 12 min talk, and since this talk is quite short, we decided that there will be no questions during the talks, but there will be the opportunity to ask one or 2

9
00:02:03.810 --> 00:02:18.369
Kristina Giesel: short, clarifying questions after the individual talks. Then each speaker of the Symposium will ask one question to one of the other speakers in the Symposium. So there will be 3 questions in this circle round.

10
00:02:18.550 --> 00:02:41.020
Kristina Giesel: And then finally, we will have an open discussion with the audience. Yeah, there can be more questions to the talks, but we also hope that other people will contribute to work on non-singular black coats, because, of course, the symposium only gives a selection of the work that is done in our community. And it would be wonderful if more people contribute to the discussion.

11
00:02:41.450 --> 00:02:49.849
Kristina Giesel: So with this. Yeah, we will start with our 1st speaker, Francesco. I will stop sharing the screen, and then the stage is yours.

12
00:02:51.080 --> 00:02:52.260
Francesco Fazzini: Thanks, Christina.

13
00:02:59.140 --> 00:03:02.919
Francesco Fazzini: Okay. Do you see my slides? My screen.

14
00:03:03.680 --> 00:03:04.359
Hal Haggard: Yes, it looks.

15
00:03:04.360 --> 00:03:05.210
Kristina Giesel: Yes.

16
00:03:05.600 --> 00:03:06.770
Francesco Fazzini: Would that be?

17
00:03:07.250 --> 00:03:26.230
Francesco Fazzini: Okay? Hi, everyone. Thanks to Christina for the nice introduction to the organizers for this opportunity and for the to the ones that are attending, I will present stellar collapse, and she, crossing singularities, ineffective loop, quantum gravity. Now

18
00:03:26.230 --> 00:03:49.690
Francesco Fazzini: let me start by the simplest possible star collapse model. That is the open one in which we consider an initial profile. That is, a step function fundamentally, in which the discontinuity of the function gives the location of the stellar boundary at initial time, and this kind of problem has been

19
00:03:49.690 --> 00:04:14.269
Francesco Fazzini: faced in the past at defective level. So through quantum corrections to the classical Einstein equations, employing different techniques and different polymerizations like the one. The 1st one. Equations of motion in interior form in differential form is right junction conditions, gluing techniques or a mix of these techniques.

20
00:04:14.550 --> 00:04:39.399
Francesco Fazzini: Now, in my talk, I will focus on a particular polymerization scheme. That is the mu bar plus kelp quantization. And within this scheme all the approaches I mentioned before, except the integral one, agree on the interior effective dynamics of the Penamy Schneider and gives an cosmological, effective dynamics. So we have

21
00:04:39.400 --> 00:04:54.100
Francesco Fazzini: an initial phase for which the star collapses. The radius of the star decreases, and energy density increases until reaching the Planck density, and then we have the re-expansion of the star in a spherical, in a.

22
00:04:54.130 --> 00:05:07.580
Francesco Fazzini: in a symmetric way around time reversal around the bounce point. Now, the 1st question I wish to address is if the open Ms. Nadder is a realistic description of effective star collapse. And to do this I'll

23
00:05:07.890 --> 00:05:32.870
Francesco Fazzini: work. Okay. I'll work in elementary Tolman bondi coordinates which line elements takes the following form, this metric describes both the matter and vacuum region of the space time, and is important, I think, to give an interpretation to these coordinates, so we can imagine to divide our three-dimensional space at fixed time. T. In spherically concentric

24
00:05:32.870 --> 00:05:57.699
Francesco Fazzini: shells. Here we are in spherical symmetry, and we parameterize each of these shells with a certain value of the coordinate radius r bigger that is here. Now, if a shell is one of these shells is inside the matter. Distribution can be taught as a physical layer composing the star, if is outside the star instead, can be taught as a geodesic

25
00:05:57.700 --> 00:05:58.640
Francesco Fazzini: shell.

26
00:05:58.820 --> 00:06:11.709
Francesco Fazzini: Now the spacetime evolution is described in these coordinates through the evolution of the aerial radius R. That is here of the shell R. At time. T.

27
00:06:11.930 --> 00:06:33.180
Francesco Fazzini: Now this holds in general for any kind of start collapse, classical or effective. But we are interested clearly in the effective one, and the questions for the effective start collapse have been provided by the Langen group in 2023. Let me see if I can. Okay.

28
00:06:33.180 --> 00:06:57.969
Francesco Fazzini: and takes the following form. Now there are 2 interesting features regarding this equation. The 1st is that in the homogeneous sector we recover effective Lqc. And the other feature related to that clearly is that these are not Pdes. This is a set of Ods that can be quite easily solved here. Delta is proportional to the Planck area, and is given by the minimum

29
00:06:57.970 --> 00:07:22.879
Francesco Fazzini: are a gap in a Qg. M is the gravitational mass inside. Each shell of this distribution and this solution that can be derived analytically takes the following form. And an important, very important feature of this solution is that is a bouncing solution. That means that you fix a shell of your distribution. You let it evolve, and this shell will

30
00:07:22.880 --> 00:07:47.810
Francesco Fazzini: bounce when the energy density on that shell will reach the Planckian value, and then will re-expand. This seems to suggest that the Openima Snyder dynamics is a good prototype to describe star collapse, because it seems that also for generic initial profiles, because notice that this solution was for any initial profile. Not only Opener Snyder, not only Friedman, whatever kind in homogeneous.

31
00:07:47.810 --> 00:07:58.009
Francesco Fazzini: continuous, non-continuous, and but an important thing to notice here is that this solution cannot be trusted after shell crossing singularities, formation.

32
00:07:58.090 --> 00:08:05.430
Francesco Fazzini: Now, to understand this statement, one has to understand. What is, what are these chef crossing singularities.

33
00:08:05.430 --> 00:08:30.089
Francesco Fazzini: Now, to introduce this concept, I recall that in Ftb coordinates the energy density is given by the following expression, in which, at denominator you see the solution of the Einstein or effective equation depending on the theory. And that numerator you have the derivative of the mass function. That is time independent. Now, if we have these 2 conditions, so R.

34
00:08:30.090 --> 00:08:53.310
Francesco Fazzini: Prime is equal to 0 for some r at some time. T. That means that 2 shells of the distribution cross at a certain time. And if for the same r we have that M. Prime is different from 0. That means that this crossing happens in the matter region. Then, as one can see notice here easily, rho diverges and also curvature scalars diverge.

35
00:08:53.310 --> 00:09:18.299
Francesco Fazzini: Now this means that the shek crossing singularity forms. This is a physical singularity, and is called the weak, because tidal forces do not diverge close to the singularity. Now, in classical gr many initial configurations develop this kind of singularity. This is not an effective feature. This is something that happens also at the classical level, but one in the classical

36
00:09:18.300 --> 00:09:36.789
Francesco Fazzini: can choose suitable initial profiles that don't develop this kind of singularities, and this has been proved in the eighties by Lake. So the question now is, if this kind of singularities can be avoided also in a defective level, and the answer is no.

37
00:09:36.930 --> 00:10:01.040
Francesco Fazzini: And this is provided by the following theorem for the marginally bound case. That means epsilon equals to 0 a shek crossing. Singularity will necessarily form at some r. If the initial energy, density, profile is non-negative, continuous of compact support, and for which M is not everywhere at 0. This one can easily realize that are very reasonable assumptions for realistic star collapse.

38
00:10:01.040 --> 00:10:25.959
Francesco Fazzini: and similar results can be obtained for non-compact profile, but with enough large homogeneities, for example, the cosmological one and the homogeneous one does not develop this kind of singularities. Here I give a numerical example, to understand concretely what are the short crossing singularity? Imagine to take an initial profile that in this case is not bounded as not compact.

39
00:10:25.960 --> 00:10:48.330
Francesco Fazzini: is a hyperbolic tangent, and we let it. We let it evolve now, as you can see here, the shells on the core of the distribution for which the energy density is almost flat, the profile is almost flat, will bounce as in accuracy, and we follow their dynamics in the future, and will expand after the bounce.

40
00:10:48.330 --> 00:11:11.550
Francesco Fazzini: But if you look at the shells, the colored one, so the ones that are on the tail of this distribution, they will cross the ones that have already bounced of the core, and will produce shed crossing singularities. This is the general picture that time that I worked on, and the idea behind this is quite easy to be understood.

41
00:11:11.550 --> 00:11:35.610
Francesco Fazzini: The reason why this crossing happens is that when the shells on the core bounce because they reach the Planckian density, the ones on the tail. Do not have time enough time to bounce, and will cross in their collapsing phase during their collapsing dynamics, the ones on the core that already bounced, and shell crossing. Singularities form.

42
00:11:36.060 --> 00:11:57.889
Francesco Fazzini: Now this can be, we proved, together with Lorenzo, and that the same happens for the non marginally bond cases. So epsilon different from 0, and this means that the open model for this particular framework, so new bar plus kilo quantization scheme is not a good prototype for dust collapse.

43
00:11:57.890 --> 00:12:21.199
Francesco Fazzini: Now, one can ask, okay, this is for dust. What happens if we consider more general initial profiles provides with pressure. Since this crossing happens between 2 shells. One can imagine that once pressure is kept in account pressure, maybe, is able to prevent this crossing, so does not allow these shells to cross.

44
00:12:21.200 --> 00:12:46.110
Francesco Fazzini: and what we found recently is that this is not the case, so pressure does not change the picture. We derived these results by constructing equations of motion in Ltb coordinates that hold both for perfect fluids, non-perfect fluids, linear equation of state, nonlinear equation of state, so polytropic or whatever. And here I will show

45
00:12:46.110 --> 00:12:54.819
Francesco Fazzini: only results regarding the the perfect fluid for a linear equation of state. Here I show true

46
00:12:54.820 --> 00:13:19.629
Francesco Fazzini: different initial energy, density profiles, both decreasing and the dynamics for different values of Omegas, so different magnitudes of the pressure, both positive and negative. Omegas, as you can see here when, for example, looking at this one, this plot here, when the shells on the core bounce the ones that are on the tail do not

47
00:13:19.630 --> 00:13:44.240
Francesco Fazzini: have time to bounce also with very large pressure. Here we have Omega, 0 point 4, and shell crossing. Singularities arise here as a side. The dynamics numerically cannot be extended after shell crossing singularities because the shell dynamics is not decoupled, and the fact that our partial differential equation produce divergences that propagate and

48
00:13:44.240 --> 00:14:09.220
Francesco Fazzini: the dynamics breaks down. But the picture is exactly the same. This does not change anything qualitatively. This means these results suggest at least that shek crossing singularities seem to be a general feature of star collapse, at least for this effective model. I'm not inferring about other kind of effective models in which maybe the open Ms. Neither profile and the premise

49
00:14:09.220 --> 00:14:18.590
Francesco Fazzini: solution remains a valid example, a valid prototype also for more general collapse. But here is not the case

50
00:14:19.470 --> 00:14:33.990
Francesco Fazzini: now, to conclude, I showed you that sheik crossing singularities are a central feature of stellar collapse within the new bar, plus kilo quantization scheme, both in the dust and fluid.

51
00:14:34.140 --> 00:14:59.009
Francesco Fazzini: Now, then, the premise neither is not a good description for seller collapse, at least within this scheme. Now there are many questions that are open that are not answered. Yet. The 1st is how to extend the dynamics beyond this sharecrossing singularities, and this can be done because the weak nature of this singularity, one possibility is through weak solutions.

52
00:14:59.010 --> 00:15:16.209
Francesco Fazzini: If a particular question of State can remove shek crossing singularities within this model. Until now we found that this is not the case. But who knows? Maybe there are particular kind of questions of state, maybe polytropic. That play this game here.

53
00:15:16.210 --> 00:15:41.130
Francesco Fazzini: And that sort of the problem and other questions is, I mean, is interesting to investigate other polymerization effects inside the model or other polymerizations at all. For example, the one proposed by Mika in his talk, both in openms neither, and beyond that, and also other more fundamental approach, like Gft. To conclude also an important

54
00:15:41.130 --> 00:15:59.200
Francesco Fazzini: question, that is open is, what is the role of oaking radiation here? I mean this computation I showed do not contain any anything about the oaking radiation, and in principle we do not know if it plays a role during the dynamics. And with this. Thank you for the attention.

55
00:16:01.240 --> 00:16:11.740
Kristina Giesel: Thank you very much, Francesco, perfectly on time. So we have time for one or 2 questions. Are there questions currently from the audience?

56
00:16:15.640 --> 00:16:16.330
Western University: Thanks.

57
00:16:16.710 --> 00:16:18.890
Western University: Do you take questions from?

58
00:16:19.950 --> 00:16:22.170
Western University: Consider you take questions from everybody.

59
00:16:22.480 --> 00:16:24.099
Kristina Giesel: From everybody. Now, yeah.

60
00:16:24.460 --> 00:16:25.720
Western University: I have a question.

61
00:16:25.890 --> 00:16:26.290
Francesco Fazzini: Yeah.

62
00:16:26.290 --> 00:16:27.619
Kristina Giesel: Yeah. Please. Go ahead.

63
00:16:28.344 --> 00:16:42.189
Western University: There's 1 thing I I'm confused, Francesca. Maybe you can. You can clarify this if the initial profile is the one of the original. Os model, namely, constant. Yeah. The one in your 1st slide

64
00:16:43.310 --> 00:16:46.020
Western University: do cross and singularity develop.

65
00:16:47.891 --> 00:16:50.779
Francesco Fazzini: Yeah, what develops are shed crossings.

66
00:16:50.780 --> 00:16:52.480
Western University: Help. Close and similarity develop.

67
00:16:52.480 --> 00:17:02.039
Francesco Fazzini: No, no physical singularities? No. Now, in this case, no, this is the and indeed the this is the only case that is.

68
00:17:02.040 --> 00:17:03.290
Western University: Shells, cross.

69
00:17:03.530 --> 00:17:28.459
Francesco Fazzini: Yeah. 2 shells cross. Yeah, you're you're right. But one shell. The shells that cross are true. One is the one inside the star, or sorry at the boundary of the star. So this is the last shell of the star, and one is a shell in vacuum. Now the the fact that they cross sorry. The fact that they cross does not mean anything physical, because they, for me, at least because the shell in

70
00:17:28.460 --> 00:17:34.939
Francesco Fazzini: the fact that the shell in vacuum crosses. The one on the boundary

71
00:17:34.940 --> 00:17:59.930
Francesco Fazzini: can be avoided by changing coordinates in the exterior. I recall that the shells in Ftb coordinates the shells that regard the vacuum are not physical. Shells of the star are geodesic shells, that one are observers. If you wish so, in a sense, to give a physical insight about this is how to say. One observer eats the star.

72
00:17:59.940 --> 00:18:22.049
Francesco Fazzini: and what should happen physically. Nothing. I mean, he's an observer, and it's not a physical gravitating shell, and for this reason in openms neither. What happens is a shell crossing, so we have the condition, R. Prime equal to 0, but not a shef crossing singularity, so to say, the physical scalars do not diverge, and

73
00:18:22.050 --> 00:18:40.200
Francesco Fazzini: from my perspective. But this is my opinion. For example, I mean others that are working on this have different opinions from my opinion. In all Indo-pane Snyder case. These models predict

74
00:18:40.200 --> 00:19:00.289
Francesco Fazzini: from my perspective the correct dynamics, but only in openm. This is the point only in openms. Neither, if we go a bit beyond openms, neither even slightly, even for any profile for any. If you wish perturbation of open Ms. Neither you. You end up with crossing singularities. And so the dynamics.

75
00:19:00.290 --> 00:19:06.250
Western University: Understand, this is clarifying. So in the exact Oppenheimer Slider you mean in this internal

76
00:19:06.430 --> 00:19:10.319
Western University: in the inside of the star there's no shell crossing.

77
00:19:10.320 --> 00:19:12.180
Francesco Fazzini: Exactly. Exactly. Yes.

78
00:19:12.180 --> 00:19:17.360
Western University: And why so? Because intuition is the same right? Why doesn't the core bounces first, st and then the.

79
00:19:17.360 --> 00:19:45.770
Francesco Fazzini: Sure, sure, because these shells and this is clear in this simulation. Here, as you can see, the shells on the core here is not openms neither, but the interior is quite. I mean, I would be a good approximation here for the interior. All the shells bounce at the same time, and the same happens in cosmology, in cosmology. Shef crossing this for homogeneous profile don't arise for exactly the same reason. They bounce all at the same time.

80
00:19:45.770 --> 00:19:49.390
AAipad2022: Okay. So they do not cross. So it's just homogeneity correct. I mean.

81
00:19:49.390 --> 00:19:52.890
Francesco Fazzini: Yes, is in the marginal sector. Yeah, exactly. Yes.

82
00:19:53.020 --> 00:20:12.670
Francesco Fazzini: Is the homogeneous sector, I mean. Otherwise we will not be in a naive argument. We would not recover in our homogeneous sector accuracy that, instead, is manifest from these equations, these equations in the homogeneous sector give accuracy. So yeah.

83
00:20:13.290 --> 00:20:13.840
Francesco Fazzini: I don't.

84
00:20:13.840 --> 00:20:30.219
Western University: And couldn't they bounce on the same time with another dynamics? All the shells? I mean time, here is an arbitrary choice of time, so couldn't there be a time such that the bounces, all at the same time, could be chosen time.

85
00:20:30.220 --> 00:20:39.119
Francesco Fazzini: No, no, I mean, you can change coordinates for the interior and make them bounce at different times for your slice. But what? What? Yeah, right for sure.

86
00:20:39.120 --> 00:20:39.760
Western University: Sure.

87
00:20:40.100 --> 00:20:48.040
Francesco Fazzini: But they, I mean, if they do not cross, these are physical shells, so if they do not cross in in a gauge, they do not cross in any other.

88
00:20:48.040 --> 00:20:53.619
Western University: Okay, I understand. So for you, what the key point is a divergence of of what the the

89
00:20:53.620 --> 00:20:55.560
Western University: the density, energy, density.

90
00:20:55.560 --> 00:20:57.259
Francesco Fazzini: Yeah, yeah, they were just.

91
00:20:57.260 --> 00:21:08.469
Western University: If the energy density goes up, don't we expect quantum gravity to present prevent? This is our basic intuition of the quantum gravity is exactly what at some point makes our bounded.

92
00:21:09.040 --> 00:21:15.302
Francesco Fazzini: Yeah, yeah, I expected. The point is that this model is not able to capture this kind of

93
00:21:16.107 --> 00:21:22.509
Western University: Okay, okay. So it doesn't prevent the so that particular dynamics that you're considering.

94
00:21:22.680 --> 00:21:24.529
Western University: Yeah, that doesn't

95
00:21:24.670 --> 00:21:32.700
Western University: doesn't do. What some may consider is, is intuitively that has to happen, which is quantum. Gravity bounds the

96
00:21:33.170 --> 00:21:35.030
Western University: energy density to some maximum.

97
00:21:35.030 --> 00:21:44.979
AAipad2022: Yeah. Can. Can I just interrupt you just for a second, because I just might be clarifying. There's a nice analysis by what I'm saying about. You know this singularities in general, and the point is that if these

98
00:21:45.200 --> 00:22:09.080
AAipad2022: low quantum gravity effects don't seem to cure the weak curvature, singularity, and this, I think, is a weak curvature singularity, and if I just spoke and correct me so, if and so, the statement is that the weak curvature singularities will be made, but in some sense, then one should not be so worried about it physically, anyway, because, as you said, this doesn't mean that anything is going to be ripped apart right.

99
00:22:10.170 --> 00:22:35.730
Francesco Fazzini: Sorry to continue. I mean the difference from the firstly, to for the audience to clarify, shell focus in singularities here are avoided, so loop quantum effects prevent the shell focus in singularity. But polymerization. This kind of polymerization that are introduced here do not prevent that kind of weak singularities. Now.

100
00:22:35.730 --> 00:22:38.200
Western University: Yeah, that's very clear. Thank you, Francesco. That clarifies a lot.

101
00:22:38.200 --> 00:22:38.760
AAipad2022: Yeah.

102
00:22:40.680 --> 00:22:53.770
Kristina Giesel: Okay, thank you. I think we should move on. Of course there's time for further questions. After all, speakers have been given their talks. So I would like Michal to share his screen.

103
00:22:55.160 --> 00:22:56.330
Michał Bobula: Yes, yes.

104
00:23:02.140 --> 00:23:04.020
Michał Bobula: let me go. Full screen.

105
00:23:05.810 --> 00:23:13.399
Michał Bobula: Yes, so thank you for the introduction. The title is the cosmic inflation prevents black Hole singularity, formation.

106
00:23:13.400 --> 00:23:37.439
Michał Bobula: So I will talk about the modified Oppenheimer's. Neither collapse, scenario and the modification will be different than the one mentioned in the Francesco stock, namely, here, in my model. The exterior by assumption will be the regular Hayward black hole, and I will try to answer the question, what will be the corresponding frw geometry, namely, what will be the properties of the interior

107
00:23:37.440 --> 00:23:53.580
Michał Bobula: universe? Homogeneous spatiality, flat universe. And I will also ask how well the corresponding frw geometric could describe our universe. So what is the vocabular black hole? This can be regarded as a quantum, corrected partsheet metric.

108
00:23:53.730 --> 00:24:08.849
Michał Bobula: namely, the here you have a comparison between the Schwartzheit and Hayward metric function, so you can see at the origin of the rudder. Coordinate. The metrics are very different. The Hayward is regular, it behaves like the the sitter

109
00:24:09.030 --> 00:24:38.999
Michał Bobula: or small values of the radial coordinate. So yeah, the question is, what would be the interior cosmology in this modified code of Oppenheimer Snyder? So there are 2 descriptions that deliver Hayward black hole as a unique vacuum solution, because in this, in my model the Hayward black hole will be treated as a vacuum solution. The 1st description is the description defined in spacetime dimensions, d. Larger or equal than 5. This is quasi topological gravity. This is the Einstein, Hilbert action

110
00:24:39.050 --> 00:24:51.019
Michał Bobula: supplemented with infinite tower of higher curvature corrections. These corrections are constructed so that the equations of motions remain, or the second order is very cosymmetric.

111
00:24:51.110 --> 00:25:04.960
Michał Bobula: The other description is the polymer, polymerized Ltb framework. There is a specific unbunded. What is important? Polymerization function that deliver Hayward blackhore as a unique fucking solution.

112
00:25:05.580 --> 00:25:21.059
Michał Bobula: So why Hayward? On the left you can see the static Hayward black hole solution. It resembles the reister-nordstrom solution. However, the origin of the radial coordinate is regular, and on the right you can see the formation and evaporation

113
00:25:21.060 --> 00:25:41.249
Michał Bobula: of the Hayward black hole, and I believe that the paper of Hayward got so much attention in the literature, because there will be no black Hole information paradox in this spacetime, namely, here, at this infinity, future infinity. I believe there will be enough cauchy data to reconstruct what has happened in the past.

114
00:25:41.250 --> 00:25:47.959
Michał Bobula: So in that sense, I believe this diagram is compatible with the Ashtekar Boyevelt

115
00:25:48.010 --> 00:25:58.110
Michał Bobula: paradigm for the black hole evaporation. And this is remarkable that the buck reaction, actually including the buck reaction, makes the space-time globally hyperbolic.

116
00:25:59.030 --> 00:26:22.880
Michał Bobula: Okay, so what is my model? The exterior is the hybrid black hole by assumption, and the interior Frw. Will be fully determined by the junction conditions with the exterior. I assume that the energy, conservation, energy, momentum, conservation holds for dust. In particular, the relation between density and mass and volume is the following.

117
00:26:23.150 --> 00:26:30.129
Michał Bobula: and I believe these are, these assumptions are compatible with quasithropological gravity and the polymerized Ltb. Space time.

118
00:26:30.200 --> 00:26:58.610
Michał Bobula: So we have the Hayward in the exterior, and the job is to determine the interior cosmology. What are the junction conditions? The junction conditions, I call it minimal geometric requirement. I require that the metrics are c, 1 smooth at the junction surface, so that the induced metric coincide at the junction surface. The junction surface is the surface of the collapsing delta, and also the actresic curvatures coincide on the surface, and these are the standard Israel

119
00:26:58.690 --> 00:27:24.490
Michał Bobula: Junction conditions. So what are the results? We obtain? The following modified Friedman equations, where here you have the here in the red is the marked correction. L is the planck length, and you can see that when we expand the right hand side around small row or small L Square Row, we have the following series, which looks like the classical

120
00:27:24.590 --> 00:27:36.590
Michał Bobula: classical park, plus infinite tower of the higher order, corrections. On the right you can see the scale factor, the phase derivative versus the proper time, and finally the Hubble rate.

121
00:27:37.160 --> 00:27:46.109
Michał Bobula: So there will be no curvature. Singularity. The kretschman's color is bonded everywhere, even when the scale factor goes to 0 in the limit where

122
00:27:46.110 --> 00:28:08.479
Michał Bobula: time T goes to infinity, we have a 2 bounded Christmas color. So the universe is time, like geodesic time, like geodesic, you compete. The free, falling observers, co-moving observer fall for infinite proper time, and we can see that we have a smooth transition from power law contraction to the inflationary phase with the graceful entrance to the inflation inflation. Let's say

123
00:28:08.550 --> 00:28:10.449
Michał Bobula: so. The energy density

124
00:28:10.550 --> 00:28:23.490
Michał Bobula: obviously diverges in the at the final collapsing point where T goes to T goes to infinity. Let me elaborate it more on the next slide, because here you can see the

125
00:28:23.510 --> 00:28:42.370
Michał Bobula: conformal diagram for this modified Oppenheimer Snyder collapse scenario. The collapse starts here. R equal rb, is the surface of the collapsing dust ball R equals to 0. Here is the origin of the radial coordinate. So we have a 2 horizons X plus and X minus.

126
00:28:42.630 --> 00:28:46.709
Michał Bobula: Here is the inner horizon. We have a event horizon here.

127
00:28:48.020 --> 00:28:55.199
Michał Bobula: so the collapse lasts forever as measured by the co-moving observers for the dust ball.

128
00:28:55.310 --> 00:29:16.580
Michał Bobula: The final collapsing point is the point actually on the conformal diagram is located here, and remarkably there is unique, only unique radial nod geodesic that arrives at this point because the other radial nodulesic, according to this diagram, leave the dust ball at some point.

129
00:29:17.670 --> 00:29:42.520
Michał Bobula: and, what is more, I believe that the when we include the poking rodation to this picture, then this infinite density at the final collapsing point will be absent, because I believe that, according to the co-moving observers co-moving with the dust bulb, the black hole should evaporate infinite of time, so there will be finite energy extracted from the black hole. And this is also what

130
00:29:42.670 --> 00:29:50.130
Michał Bobula: that the platform operates in definite time. This is also what the diagram given by Hayward indicates.

131
00:29:52.760 --> 00:30:14.190
Michał Bobula: So yes, let me move to the discussion. So there are 2 descriptions that identify the Hayward black hole as a unique vacuum solution. The 1st one is the quasi topological gravity, which is the Einstein hip reduction with infinite tower of higher curvature corrections, and the second one is the framework of polymerized Ltv models.

132
00:30:14.670 --> 00:30:28.679
Michał Bobula: So what I have done I have derived the corresponding Frw dust dynamics which is viable for the interior, and here you can see that the modified Friedmann equation accounts for blank scale corrections.

133
00:30:29.410 --> 00:30:40.890
Michał Bobula: So I use the junction conditions with the exterior that allowed me to derive the unique inter geometry. So we have a let's say, long squish trajectory.

134
00:30:41.190 --> 00:31:03.339
Michał Bobula: so they collapse us forever. We have a graceful entrance to the inflationary phase in that collapse scenario. And also this modified Friedman equation admit expanding solution. Where we have a graceful, graceful exit from the inflation, then the the dynamics is time reverse. Let's say

135
00:31:03.760 --> 00:31:18.160
Michał Bobula: so. We see that we have a nice interpretation of the cosmic inflation in the collapse settings, namely, that this is a quantum mechanism that decelerates the collapsing matter and prevents it from singularity formation.

136
00:31:19.180 --> 00:31:33.940
Michał Bobula: The next thing is that the resulting dust collapse model resembles a recently one obtained within the model based on asymptotically safe gravity in that theory or in that model which is inspired by asymptotic safety.

137
00:31:33.940 --> 00:31:50.410
Michał Bobula: The coupling between the matter and gravity is a running, coupling, and the gravity becomes weaker and weaker, the higher the energies are, so the so so at the physical picture will be very similar, and I believe that the conformal diagram. The qualitative features are

138
00:31:50.410 --> 00:31:51.780
Michał Bobula: exactly the same.

139
00:31:52.240 --> 00:32:10.390
Michał Bobula: so we have a lesson for cosmology, so that the finite universes which are surrounded by black hole vacuum may circumvent, bore theory which states that the inflationary space-time are past or future incompete. Why do I mention this

140
00:32:10.570 --> 00:32:39.050
Michał Bobula: this thing? Because this modified Friedman equation in the model beyond Oppenheimer Snyder. When we have an infinite universe, they will deliver the singular universe. However, when the universe is finite and surrounded by the black hole vacuum. The trm of Portugal Wienkin is circumvent, so that the whole spacetime would remain geodesically complete.

141
00:32:39.900 --> 00:32:48.010
Michał Bobula: And finally, how well the cosmological dynamics can describe our universe do we live inside a hybrid black hole?

142
00:32:48.880 --> 00:33:07.140
Michał Bobula: And I believe it is particularly important to compute the hoking gradation, because only with the computed hawking gradation or introduced hawking gradition. We can address the local information paradox, and I believe this topic will be discussed more in the honest talk.

143
00:33:07.930 --> 00:33:09.360
Michał Bobula: Thank you for attention.

144
00:33:12.110 --> 00:33:20.189
Kristina Giesel: Thank you very much, Michal. Again we have time for a few questions directly to the speaker. Now

145
00:33:20.810 --> 00:33:24.230
Kristina Giesel: I see a hand raised at Western. Is this.

146
00:33:24.400 --> 00:33:33.119
Western University: Yeah, this is Carla again. It's a short question. Michael. This is very nice. Thank you. There's 1 thing I've missed.

147
00:33:33.400 --> 00:33:43.850
Western University: If you you talked about what might happen if there is a hawking radiation included, and there's a finite lifetime of black hole. What what is your guess for the

148
00:33:44.550 --> 00:33:48.180
Western University: a conformal diagram. In that case that wouldn't.

149
00:33:48.180 --> 00:34:00.000
Michał Bobula: So, okay, so so my guess must. My naive guess would be that the guy diagram could could resemble the give the given by

150
00:34:00.310 --> 00:34:06.019
Michał Bobula: about the precise details at this point. I don't know. This is my expectation based on my intuition.

151
00:34:06.380 --> 00:34:12.789
Michał Bobula: Yeah, I I got this intuition. But does this mean that the the interior sort of

152
00:34:13.780 --> 00:34:22.120
Western University: Region flows up into the into the same asymptotic outside region.

153
00:34:23.719 --> 00:34:31.129
Michał Bobula: You mean the collapsing matter or so? What would be the fate of the collapsing matter? So right.

154
00:34:31.560 --> 00:34:36.459
Western University: What is the future of the interior? Is the same future known infinity of.

155
00:34:36.460 --> 00:34:49.099
Michał Bobula: So I see, I believe that the okay, my knife expectation is that the whole interior will become the radiation. So we'll be so there will be no

156
00:34:49.340 --> 00:34:57.250
Michał Bobula: the matter constituting the let's say the the ball of matter and the the whole ball will evaporate.

157
00:34:57.560 --> 00:35:05.589
Western University: Yeah, I. I share this intuition completely. But is that compatible with the geometry that you're suggesting for the interior.

158
00:35:07.460 --> 00:35:12.710
Michał Bobula: Oh, with this one i i don't know, because I haven't account for

159
00:35:13.280 --> 00:35:18.640
Michał Bobula: in this model. I I didn't account for the hawking gradation. So okay.

160
00:35:18.640 --> 00:35:28.230
Michał Bobula: believe that there's still a window for for obtaining such a diagram, because we can see here how the causal structure is different when we include the back reaction.

161
00:35:28.380 --> 00:35:31.490
Western University: Yeah, yeah, okay, so we're on the same page. Thanks.

162
00:35:33.460 --> 00:35:39.080
AAipad2022: I have a quick question. I'm sorry I cannot raise my hand, so whenever you have time I can ask my question.

163
00:35:39.340 --> 00:35:43.020
Kristina Giesel: Yeah, please, about go ahead. I think there's no other hand raised.

164
00:35:43.560 --> 00:35:46.146
AAipad2022: Okay? So the quick question was really about

165
00:35:47.480 --> 00:35:55.190
AAipad2022: I mean, I think what one has to worry about is really completeness of Scribe. Your final picture. 5. Right. The slide. 5.

166
00:35:55.580 --> 00:35:56.250
Michał Bobula: Yes, yes.

167
00:35:56.250 --> 00:36:09.999
AAipad2022: Or even the Haver case. I think that people don't worry about enough about completeness of the future and the infinity self after you included hawking radiation, because in the semi-classical regime, for example, is incomplete.

168
00:36:10.140 --> 00:36:16.770
AAipad2022: and one might get something like that, in which case things would be much more unresolved.

169
00:36:17.230 --> 00:36:25.580
AAipad2022: So I think it. But, on the other hand, if it is complete, then I think I would be much, much more happy with the resolution that you're proposing.

170
00:36:26.250 --> 00:36:37.039
AAipad2022: And the second just second quick point is that this really along the lines of what Carl was saying, I think that what is happening in the interior. Really the full planck regime.

171
00:36:37.190 --> 00:36:41.320
AAipad2022: There's a little place where there is going to be.

172
00:36:41.920 --> 00:36:45.830
AAipad2022: It's going to be extremely dynamical and plant scale coverage.

173
00:36:45.830 --> 00:36:46.370
Michał Bobula: Yes.

174
00:36:46.370 --> 00:36:55.550
AAipad2022: And that regime. I think it has to be treated very, very carefully, and at the moment at least, I don't think we have a good handle on treating that regime.

175
00:36:57.990 --> 00:37:01.309
Michał Bobula: Yes, I agree with you, with your remarks.

176
00:37:01.650 --> 00:37:02.680
AAipad2022: Okay. Thank you.

177
00:37:04.620 --> 00:37:14.830
Kristina Giesel: Okay, thanks, Abby. Thanks, Michal. Then I would like to ask you to stop screen sharing so that Yunas can start his talk.

178
00:37:21.700 --> 00:37:24.010
Jonas Neuser: Yes. Can you see my slides.

179
00:37:24.800 --> 00:37:26.570
Kristina Giesel: Not yes.

180
00:37:26.690 --> 00:37:28.849
Jonas Neuser: Okay. Now, okay, very good.

181
00:37:30.420 --> 00:37:42.080
Jonas Neuser: yes. So thank you for the introduction. So, as already advertised in the other talks, I'm going to talk a bit about Black Hole perturbations and back reaction.

182
00:37:42.210 --> 00:37:48.870
Jonas Neuser: And this is part of my Phd thesis, which is joint work with my supervisor, Thomas Teaman.

183
00:37:49.280 --> 00:37:57.139
Jonas Neuser: So I mean the the purpose of this talk is to to give a bit of a different perspective. So our main

184
00:37:57.300 --> 00:38:00.549
Jonas Neuser: focus is not necessarily the resolution

185
00:38:00.660 --> 00:38:03.293
Jonas Neuser: of the singularity, but to

186
00:38:04.120 --> 00:38:18.299
Jonas Neuser: well, to derive a consistent perturbation theory, including back reaction. And then, if there's a mechanism in the quantum theory through the back reaction which resolves the singularity. This has to be

187
00:38:18.580 --> 00:38:25.590
Jonas Neuser: theme, and we have some ideas of how this might work. But

188
00:38:25.820 --> 00:38:29.249
Jonas Neuser: we didn't do the concrete calculations yet.

189
00:38:29.640 --> 00:38:35.750
Jonas Neuser: Okay, so first, st I would like to start with this open question.

190
00:38:36.285 --> 00:38:49.760
Jonas Neuser: which really, I think is very or needs an answer. And this is the question what the fate of evaporating black holes is, and there are, in fact, many proposals in the literature. So there's

191
00:38:49.870 --> 00:38:54.989
Jonas Neuser: might be Black hole explosions, black hole remnants or black hole, white hole transitions.

192
00:38:55.320 --> 00:39:08.340
Jonas Neuser: And if one really wants to attempt to answer these questions, that one should probably work towards deriving a very rigorous and 1st principle, quantum gravity theory, and do some calculation there.

193
00:39:09.953 --> 00:39:15.030
Jonas Neuser: So yeah. So in loop quantum gravity, there are a lot of

194
00:39:15.310 --> 00:39:18.190
Jonas Neuser: studies on black holes by many authors.

195
00:39:19.000 --> 00:39:23.070
Jonas Neuser: and we also saw 2 talks today by Francesco and Michal on the topic.

196
00:39:23.650 --> 00:39:31.849
Jonas Neuser: and the idea in these talks and and the loop quantum gravity. To to study black holes is to do a symmetry reduction, and then

197
00:39:32.476 --> 00:39:47.480
Jonas Neuser: study the spherical symmetric sector, and then the main focus of many models is to see how the singularity is avoided. So for example, in this this approach, based on quantum cosmology, where one takes

198
00:39:48.070 --> 00:39:58.009
Jonas Neuser: the advantage of the Kandowski-sachs cosmology, or one can study modified classical equations of motion and analyze numerically dust, collapse

199
00:39:58.170 --> 00:40:01.309
Jonas Neuser: scenarios, or we can do spin form numerics

200
00:40:01.720 --> 00:40:13.139
Jonas Neuser: with black hole to white hole transitions. And also recently, there's work going beyond this spherical symmetric sector and also consider perturbations in this Kandowski-sachs interior

201
00:40:13.350 --> 00:40:14.782
Jonas Neuser: in this talk

202
00:40:15.720 --> 00:40:35.289
Jonas Neuser: the goal is to derive from consistent framework for black hole perturbation theory, including back reactions. So we want to consider the full phase space of general relativity and potentially some matter. Then we would like to treat the symmetric sector exactly, and then, of course, a non-symmetric sector can only be treated

203
00:40:36.000 --> 00:40:41.039
Jonas Neuser: perturbatively. Then we want to incorporate back reaction effects.

204
00:40:41.270 --> 00:40:45.599
Jonas Neuser: so that we have the interaction between the non-symmetric and the symmetric sector and

205
00:40:46.262 --> 00:40:54.300
Jonas Neuser: we want to consider reduced space-base formulation, so that we have a well-defined quantum theory without anomalies.

206
00:40:54.720 --> 00:41:03.009
Jonas Neuser: and then in the future we. They put the the purpose of this is to apply it eventually to hawking evaporation.

207
00:41:03.810 --> 00:41:24.819
Jonas Neuser: So how does this work? So? First, st we consider some symmetry groups. So for black holes, it's very logical to go to a spherical symmetry, and also arguments show that the angular momentum is radiated away much faster than the mass. So this is also a good approximation for the late stage evaporation.

208
00:41:25.250 --> 00:41:35.149
Jonas Neuser: Now, of course, in the canonical formulation of gr, we have the induced metric and its conjugate momentum, and then we can expand them into scalar vector and tensor harmonics.

209
00:41:35.750 --> 00:41:49.739
Jonas Neuser: We have, then the 0 modes which are the symmetric variables, and we denote them by Q and P. And we have the non-symmetric variables which come from the modes L bigger than 0, and we use the notation X and y.

210
00:41:50.080 --> 00:42:04.300
Jonas Neuser: then we can decompose the full constraints of this theory into these 0 modes here, which we call C, and the non-symmetric constraints which we obtain by averaging over.

211
00:42:04.510 --> 00:42:10.499
Jonas Neuser: or by integrating with these spherical harmonics, to obtain these non-symmetric constraints instead.

212
00:42:10.840 --> 00:42:15.500
Jonas Neuser: And finally, we can also split the test function into the symmetric ones and the non-symmetric ones.

213
00:42:17.620 --> 00:42:34.959
Jonas Neuser: So once we've done this analysis of the symmetry. We also have to deal with vacation variance. So there we can do a second splitting of the Observables and the into the observables and the non-observable degrees of freedom. So in total, we get these

214
00:42:35.070 --> 00:42:37.139
Jonas Neuser: 4 sectors in this table.

215
00:42:37.450 --> 00:42:44.089
Jonas Neuser: so the Observables will be with these capital letters and the non observable ones with the small letters.

216
00:42:45.320 --> 00:42:54.970
Jonas Neuser: Okay, so this is how we decompose our phase space. And then, of course, we apply the reduced phase space formulation.

217
00:42:55.370 --> 00:43:01.320
Jonas Neuser: And there we use the constant Pan levy guide get fixing. So we fix

218
00:43:01.690 --> 00:43:04.759
Jonas Neuser: the little Q and the little X

219
00:43:05.290 --> 00:43:11.020
Jonas Neuser: to some specific values which come from this gauge.

220
00:43:11.460 --> 00:43:15.739
Jonas Neuser: and then we solve the constraints perturbatively. So we solve

221
00:43:16.010 --> 00:43:26.640
Jonas Neuser: C equals to 0 for P and set equals to 0 for y, and then, finally, we have to determine. The Lagrange multipliers by imposing the stability condition of the gauge. Fixing.

222
00:43:28.510 --> 00:43:31.843
Jonas Neuser: then it is very important to note that

223
00:43:32.400 --> 00:43:42.310
Jonas Neuser: we have. We are in the asymptotic scenario. So we can, or we have to impose boundary conditions on the field, so that the Hamiltonian theory is well defined.

224
00:43:42.650 --> 00:43:51.740
Jonas Neuser: and then we need to require some bound counter boundary terms to obtain a well defined theory.

225
00:43:53.950 --> 00:43:56.089
Jonas Neuser: Finally, we have to.

226
00:43:56.430 --> 00:44:20.069
Jonas Neuser: or we derive the physical Hamiltonian. So if we have any function of these observable degrees of freedoms, Qp. X. And y. Then we require this function. F to have the same Poisson bracket with the physical Hamiltonian as it has with the sum of these constraints and the boundary term. If we go to the constraint surface, the gauge we chose, and we impose the stabilized

227
00:44:22.070 --> 00:44:25.180
Jonas Neuser: Lagrange multiplier.

228
00:44:26.180 --> 00:44:37.620
Jonas Neuser: So if we do the calculation very explicitly, we find the following solution, so the 1st or the 0 order contribution is not surprisingly the

229
00:44:37.740 --> 00:44:45.340
Jonas Neuser: Adm mass, or the the mass of the black Hole, and then we get these quadratic contributions

230
00:44:45.590 --> 00:44:46.345
Jonas Neuser: which

231
00:44:47.460 --> 00:45:01.240
Jonas Neuser: involves like a sum of all the modes. And then we have these Yk and Xk variables. And importantly, there's this potential Vk here, which also shows up in the standard black hole perturbation theory.

232
00:45:02.980 --> 00:45:10.030
Jonas Neuser: So some remarks. So the Black Hole perturbation theory is, of course, very well established. The second order in the literature

233
00:45:10.190 --> 00:45:18.990
Jonas Neuser: and our results here. They agree with these works. If we transform to these Gp coordinates and we neglect the back reaction.

234
00:45:20.800 --> 00:45:32.350
Jonas Neuser: Okay, so what are the advantages? So the formalism is generalizable to many situations like cosmology, Schwarzschild black holes and curved black holes. By just changing the symmetry group.

235
00:45:32.810 --> 00:45:40.339
Jonas Neuser: Then we disentangle the definition of the observables from the perturbation. Theory. So we defined what is an observable and

236
00:45:40.896 --> 00:45:49.800
Jonas Neuser: what is what are the gauge degrees of freedom, independent of perturbation theory? And so we don't have to discuss gauge invariance at every order.

237
00:45:50.540 --> 00:46:04.860
Jonas Neuser: then we find that the Hamiltonian can actually be computed in X and Y to any order. So we did the explicit computations to second order. But there's no like. There's no technical issue with pursuing it to higher orders.

238
00:46:05.790 --> 00:46:10.189
Jonas Neuser: Then we have a full reduction, and

239
00:46:10.730 --> 00:46:23.029
Jonas Neuser: for the and obtain the physical Hamiltonian. So there are no constraints left in the quantum theory, and because of this there's also no issues with any constraints not closing in the quantum theory, so there are no anomalies.

240
00:46:24.210 --> 00:46:38.279
Jonas Neuser: The next step, of course, is to to perform a quantization with respect to this Gaussian Levi free falling observer. So we, the plan or one strategy, might be to quantize the perturbations using a fog quantization, and then

241
00:46:38.430 --> 00:46:46.970
Jonas Neuser: the mode functions will satisfy some eigenvalue equation which is similar to Schrodinger equation with singular potentials. And then.

242
00:46:47.120 --> 00:47:02.939
Jonas Neuser: of course, there's the singularity at R equals to 0. So possibly we need to do some regularization there. So, for instance, one can think about using some orthonormal basis for singular shooting operators.

243
00:47:03.170 --> 00:47:14.980
Jonas Neuser: or we can get inspired by what people do in loop quantum gravity, for example, on the Kandowski sacks, quantization, or of what what people working on dust collapse

244
00:47:15.140 --> 00:47:17.080
Jonas Neuser: models use.

245
00:47:18.340 --> 00:47:24.489
Jonas Neuser: So, to sum it up. So we developed a novel and 1st principle approach to Black Hole

246
00:47:24.870 --> 00:47:28.180
Jonas Neuser: have operational perturbation theory, which includes

247
00:47:28.290 --> 00:47:37.870
Jonas Neuser: back reaction, the exterior and interior. Simultaneously, then, we plan to to quantize it. So we have quantized gravity, then.

248
00:47:38.460 --> 00:47:53.230
Jonas Neuser: well, we have a perturbation, dependent definition of the observables, and we can expand our formalism to arbitrary orders, and for the future. We plan to generalize to higher orders and get interacting gravitational waves.

249
00:47:53.640 --> 00:48:04.060
Jonas Neuser: We would like to have a look at other boundary observers at infinity and make, maybe some contact with people working on the Bms group to to constrain the quantum theory.

250
00:48:04.400 --> 00:48:14.870
Jonas Neuser: We also plan to extend to other standard model matter. We already discussed the electromagnetic field. But of course, new genomes are also important.

251
00:48:15.790 --> 00:48:21.189
Jonas Neuser: Then we can generalize to access symmetry like the current black hole. And

252
00:48:21.780 --> 00:48:27.240
Jonas Neuser: and then, of course, we also have to explicitly do the computation of the quantization.

253
00:48:27.340 --> 00:48:35.880
Jonas Neuser: And if we if if we done the quantization, then we can apply the framework to study evaporating black holes.

254
00:48:36.570 --> 00:48:41.320
Jonas Neuser: And with that I'm I'm done and happy to take some questions.

255
00:48:44.200 --> 00:48:52.300
Kristina Giesel: Yeah, thank you very much, Jonas. I see again a hand raised at Western University. So please go ahead.

256
00:48:53.210 --> 00:49:06.260
Western University: Me if there's nobody else. Thank you. There is a there is this is very nice. I mean, you guys do things over systematically and and solidly. But because of that.

257
00:49:06.550 --> 00:49:12.689
Western University: I wonder I have a worry that I wonder if you have considered it, and let me try to to express it.

258
00:49:13.559 --> 00:49:19.950
Western University: You fix the ghoulstrampane levee gauge at the very beginning.

259
00:49:20.340 --> 00:49:32.200
Western University: Now, what in our experience, what what happens? It's it's the following, if if I if if we study some of the geometries

260
00:49:32.400 --> 00:49:38.139
Western University: that come from other guesses of what could happen, some effective geometry that could.

261
00:49:38.340 --> 00:49:49.839
Western University: And we look at the gauge. This correspond to fixing coordinates that do not cover entire spacetime, in fact, that

262
00:49:49.980 --> 00:50:14.360
Western University: go bad where the interesting stuff happened. And and this is this is something also came out in in the discussion with Francesco before. As Francesco said at the beginning. In the pure OS case there was a apparent phenomenon that happened by an analysis in those coordinates that turn out to disappear

263
00:50:14.560 --> 00:50:34.859
Western University: just because it was a coordinate artifact. So the question is, or the worry. The advice is, be careful, because in in those coordinates you might already have made a choice that prevents you to evolve in the regions where interesting stuff happened.

264
00:50:35.920 --> 00:50:41.193
Jonas Neuser: Yes, yes, thank you for that. Of course. Fixing like a gauge is always

265
00:50:41.720 --> 00:50:53.369
Jonas Neuser: problematic in in the way you explained. So in fact, like the the, this coordinates only cover, like either the infalling.

266
00:50:53.940 --> 00:51:01.359
Jonas Neuser: Sector or the outgoing sector, so so they cannot cover, like both of these simultaneously. So one needs to.

267
00:51:01.360 --> 00:51:04.069
Western University: This is the facetime getting the bounce.

268
00:51:05.570 --> 00:51:06.290
Jonas Neuser: Sorry.

269
00:51:06.470 --> 00:51:11.880
Western University: They might have difficulties, this coordinate of capturing the bounce because they go wrong at the bounce. Yes, if they.

270
00:51:11.880 --> 00:51:16.929
Jonas Neuser: Yes, 1 1 needs to to be careful at that point. Yes, that's do.

271
00:51:17.100 --> 00:51:17.610
Western University: Okay.

272
00:51:17.610 --> 00:51:30.239
AAipad2022: So it it seems to me that there really are the 1st 2 talks, and and this talk are complementary to each other, or, if you like it, orthogonal to each other, and we need to superpose them appropriately, because in this talk one is not considering collapse.

273
00:51:31.430 --> 00:51:36.459
AAipad2022: In this talk one is considering really perturbations on Black Hole backgrounds.

274
00:51:37.390 --> 00:51:40.340
AAipad2022: and please correct me at the end.

275
00:51:41.360 --> 00:51:45.759
AAipad2022: So, therefore, these considerations that were

276
00:51:46.120 --> 00:51:49.609
AAipad2022: important in the 1st 2 talks are not really important here.

277
00:51:50.160 --> 00:51:53.860
AAipad2022: so that means that this is really much better suited not to

278
00:51:54.150 --> 00:52:17.060
AAipad2022: black Hole, form back collapse, and then evaporating, but rather it might be better suited to something like the hart hawking vacuum, that is to say, you got an eternal black hole, and we just want to understand, you know what happens, or, if you like, it is more like what was done in the effective theory by, you know Almeido Singh and me rather than a collapsing situation.

279
00:52:17.390 --> 00:52:29.450
AAipad2022: So it's really, how is quantum geometry going to be affected, going to be changed? And such things? So there's no matter here in the in this I mean, no, no matter forming the platform, there's no matter to Zeroth order.

280
00:52:29.930 --> 00:52:33.079
AAipad2022: The matter is all coming at the, at the perturbative level.

281
00:52:33.420 --> 00:52:38.769
AAipad2022: so it seems to me the 2 are really kind of complementary, or in some ways are tolerant to each other.

282
00:52:39.050 --> 00:52:47.749
AAipad2022: and they're not addressing the same problem. Do you agree with this.

283
00:52:48.710 --> 00:52:55.839
Jonas Neuser: So. Yes, I would, I would think yes, that these 2 works are very complementary, and

284
00:52:55.960 --> 00:52:57.849
Jonas Neuser: in the sense that

285
00:52:58.370 --> 00:53:10.539
Jonas Neuser: but in these, in these dust models. You really do some very hands-on computation to put it to the computer and then see how the dust collapses and and bounces back out, and we

286
00:53:10.730 --> 00:53:16.659
Jonas Neuser: our, I mean, we can also look at like let's say, the eternal black hole, and and see how the

287
00:53:17.595 --> 00:53:21.500
Jonas Neuser: how the the bake reaction works in in that case. Yes.

288
00:53:21.870 --> 00:53:22.830
AAipad2022: Yeah, thank, you.

289
00:53:23.900 --> 00:53:32.679
Kristina Giesel: Okay, we have 2 more hands raised. One is Thomas, and the other is vicar. So I think Thomas was first.st Please go ahead.

290
00:53:32.680 --> 00:53:38.670
thiemann: Yeah. So this is a reply to what Abbay just mentioned.

291
00:53:39.569 --> 00:53:46.160
thiemann: So. And it is true that in in the, in the work that we have done so far. We have just looked

292
00:53:46.700 --> 00:53:51.089
thiemann: at the electromagnetic matter, and there's not much

293
00:53:51.340 --> 00:53:54.479
thiemann: of a black hole formation process going on here.

294
00:53:54.850 --> 00:53:59.250
thiemann: But of course we want to go beyond that. So one

295
00:53:59.390 --> 00:54:04.519
thiemann: think thing one could do is to actually use the dust stuff that people are using

296
00:54:04.830 --> 00:54:15.809
thiemann: in the we're using in the previous talk. Or, more realistically, you want to look at real collapse due to standard model Meta.

297
00:54:17.060 --> 00:54:29.579
thiemann: So that's something that can be included here. And that's the whole point of this project. In order to study the back reaction between the let's say, the spherical kismatic

298
00:54:29.800 --> 00:54:33.999
thiemann: modes of the collapsing part and the radiation part that comes out.

299
00:54:34.490 --> 00:54:39.420
AAipad2022: Great, so I think it would be much better for you to look at, not desk. But look at the

300
00:54:39.580 --> 00:54:53.589
AAipad2022: by, that kind of solution or a scalar field if you like, spherically symmetric scalar field, coupled to your situation, couple to your gravitational field, and then look at that, for example, collapsing like, like, what happened with mother one's model, for example.

301
00:54:54.069 --> 00:54:59.860
AAipad2022: That might be that might be very interesting to understand. That would be, yeah. Okay. I agree with you. Yeah.

302
00:54:59.860 --> 00:55:00.510
thiemann: Exactly. Yeah.

303
00:55:02.460 --> 00:55:08.239
Kristina Giesel: Okay, thank you. Thomas and Abbai. Next one, and maybe final question now is Vika.

304
00:55:09.184 --> 00:55:23.399
Viqar Husain: Hi, thanks, Christina. This is just a comment on Carlos. Comment concerning Pg coordinates. It's possible to use Pg coordinates to get a clean phenomenological bouncing metric, and we have demonstrated that with a smooth metric.

305
00:55:23.420 --> 00:55:41.309
Viqar Husain: So I think, for the static case or very special time dependence, there might be a problem. But for the inhomogeneous case, the kind of model metric in some of the work we did presents an example where Pg. Works just fine, with

306
00:55:41.370 --> 00:55:45.229
Viqar Husain: not a sharp boundary, but in in homogeneous matter, profile.

307
00:55:49.070 --> 00:55:53.188
Kristina Giesel: Okay, thank you. Vika, yeah. Now we come to the

308
00:55:53.750 --> 00:56:06.059
Kristina Giesel: discussion among the speakers because they met before they discussed their topics and talks and had a few questions on the other, yeah, on the work of the other people.

309
00:56:06.300 --> 00:56:17.269
Kristina Giesel: So yeah, I think, Jonas, you were the last speaker. You can just start, and then it's a circle of questions, and afterwards we will open the discussion to everybody again.

310
00:56:19.170 --> 00:56:24.910
Jonas Neuser: Yes, so so actually, I. I have a question for Francesco, which is also a long

311
00:56:25.150 --> 00:56:28.380
Jonas Neuser: these lines that we we discussed

312
00:56:28.520 --> 00:56:40.520
Jonas Neuser: because I was wondering a bit like what happens if one also introduces perturbations and non symmetric degrees of freedom in these task collapse models.

313
00:56:40.700 --> 00:56:45.769
Jonas Neuser: and because 1 1 sees, or what Francesco showed is that

314
00:56:46.030 --> 00:57:03.369
Jonas Neuser: he showed that, like, even if you include the pressure, then you still get the shell crossing singularities. But of course all these models are working in spherical symmetry. So my question was, if he expects something to change, if he includes something which is non spherically symmetric.

315
00:57:04.590 --> 00:57:22.678
Francesco Fazzini: Yeah, thank you. Honest, my perspective. Clearly, one needs the model to answer to this question, to have a concrete answer. My guess is that if we consider a dynamical background, like the one that I presented with the smooth corrections.

316
00:57:23.890 --> 00:57:28.539
Francesco Fazzini: also no spherical ones, I expect that

317
00:57:28.540 --> 00:57:54.170
Francesco Fazzini: some kind of weak singularities remain because they are the background geometry that maybe can have some back reaction due to the perturbation, so on, but is, I mean there is nothing. There is no mechanism in the underlying geometry that prevents in the line theory that prevents this kind of weak singularities. My, I mean my guess is that

318
00:57:54.530 --> 00:58:03.950
Francesco Fazzini: something like that. So maybe I mean, instead of being a spherical, thin shell, maybe it's a spherical, thin shell that

319
00:58:03.990 --> 00:58:24.700
Francesco Fazzini: I mean, namely, the shell cross sensing right now is that is fundamentally set in shell with 0 volume. For this reason Rho diverges, instead of being spherical, I expect something not spherical, but that kind of I keep, and expect that kind of divergence also in this hypothetical model.

320
00:58:28.350 --> 00:58:29.470
Jonas Neuser: Okay. Thank you.

321
00:58:30.350 --> 00:59:00.059
Francesco Fazzini: Okay, I have a question to Miko in the model I would like you have. I mean the collapse that keeps going eternally, like a sort of time reverse of inflation. And yeah, my point is the matter, the volume of the star, and this is something that already by anticipated at a certain point the volume becomes

322
00:59:00.170 --> 00:59:10.840
Francesco Fazzini: Planckian sides. I mean, if if they collapse and goes forever in particular, if there is a region of accelerated collapse, sort of the sitter. I mean

323
00:59:10.840 --> 00:59:35.950
Francesco Fazzini: time, reverse this iter, and I expect that at that point defective equations break down, because I mean, as has been proved in Qc. To be valid, effective equations, and so that the fluctuations of the geometry are not kept in account. The volume of your piece of universe. In that case of our search should be large enough.

324
00:59:36.210 --> 01:00:05.129
Francesco Fazzini: and in your case, at a certain point, such limit should be broken. So yeah, my, my question is, what do you? I mean, firstly, why should we? I mean, trust in the effective dynamics at that point? And what what would be your I mean? Guess about I mean possible, a a quantum theory, I mean, our quantum theory would would work there. Yeah, what would predict.

325
01:00:06.730 --> 01:00:28.190
Michał Bobula: Okay, so thank you for this question. So the model I gave, indeed, is not a robust model, coming from some theory of quantum gravity. But my model is rather a showcase model where the concept on inflation curve could be also useful in the context on the gravitational collapse. And

326
01:00:28.350 --> 01:00:34.770
Michał Bobula: the the answer is, I don't know what will happen, or would we be able to trust

327
01:00:34.920 --> 01:00:52.449
Michał Bobula: the effective dynamics when we go beyond the lung volume, etc. But but still I believe that every model, every model, is not reliable as long as we do not include the hawking gradation in the picture, because then the dynamics could change.

328
01:00:52.550 --> 01:00:56.720
Michał Bobula: I believe, in the causal structure, so.

329
01:00:57.130 --> 01:00:57.889
Francesco Fazzini: Yeah, that is.

330
01:00:57.890 --> 01:01:02.980
Michał Bobula: And okay, yeah, yeah. And clearly, the model is not consistent with

331
01:01:03.560 --> 01:01:11.049
Michał Bobula: like, you see, in improved, in improved dynamic scheme, where we have a balance in magma collapse. We have a long squeeze.

332
01:01:11.480 --> 01:01:24.589
Michał Bobula: however, within Lqc. As far as I remember, there there are. There are some descriptions in the literature where there were inflationary space times coming from. Lqc, so maybe one could

333
01:01:24.800 --> 01:01:32.899
Michał Bobula: reconsider this this models and compute the expectation values and dispersion relations for quantum of service.

334
01:01:33.140 --> 01:01:36.290
Michał Bobula: Yeah, I hope I hope the answer is clear, clear.

335
01:01:36.520 --> 01:01:37.849
Francesco Fazzini: Okay, yeah, yeah.

336
01:01:39.370 --> 01:01:49.150
Michał Bobula: So I guess this is my turn to ask the question to Jonas. So, Jonas, you mentioned in your talk that there is a possibility for

337
01:01:49.290 --> 01:02:16.020
Michał Bobula: regularizing the black hole solution in your framework. So your framework is based on the fog quantization. So what is the picture of the black holes in the fog quantization without the reaction. So are the singularities always present in that quantization, prescription, prescription. And what is the role of the buck reaction? Can buck reaction somehow regularize this black holes.

338
01:02:17.960 --> 01:02:27.099
Jonas Neuser: So, yeah, so 1st of all, like the question, if the back reaction can resolve the singularity or not.

339
01:02:27.260 --> 01:02:34.430
Jonas Neuser: of course they can only be answered exactly if one does the computation very explicitly.

340
01:02:35.066 --> 01:02:39.329
Jonas Neuser: But so the idea we have is to to take.

341
01:02:40.370 --> 01:02:58.699
Jonas Neuser: Let's say we have the perturbations, and then we quantize them, using, let's say, a poke quantization. And then, of course, to write down this quantum theory, one needs to somehow handle the singularity at the center of the black hole, because at R equal to 0,

342
01:03:00.060 --> 01:03:09.849
Jonas Neuser: like the equation for the mode functions have a divergence. So there one would need to think about how to make sense out of this.

343
01:03:10.100 --> 01:03:14.789
Jonas Neuser: And well, there are some ideas. So so one would be to.

344
01:03:15.850 --> 01:03:29.713
Jonas Neuser: I mean the 1st question which needs to be asked. If if this poses a problem, and if it does pose a problem, then we need to work on a regularization scheme. For example. I listed like 3 ideas.

345
01:03:30.180 --> 01:03:31.929
Jonas Neuser: that we can use. So

346
01:03:33.020 --> 01:03:38.189
Jonas Neuser: the idea is to to see what what people already have done who worked on this.

347
01:03:38.330 --> 01:03:44.590
Jonas Neuser: and then maybe also what we have this application on this non singular

348
01:03:45.120 --> 01:03:48.409
Jonas Neuser: on the spaces for singular shooting operators.

349
01:03:49.283 --> 01:03:54.559
Jonas Neuser: And maybe this can be applied as a basis for functions.

350
01:03:55.910 --> 01:03:58.970
Jonas Neuser: In this black hole background. Yes.

351
01:04:04.750 --> 01:04:06.709
Jonas Neuser: Is it you? Or do you have a follow up.

352
01:04:06.710 --> 01:04:15.929
Michał Bobula: Let me graphic, clarify. So without back reaction, are the black holes singular in the effective dynamics, picture or effective description.

353
01:04:16.600 --> 01:04:18.658
Jonas Neuser: Yes, in our, in our

354
01:04:19.510 --> 01:04:25.125
Jonas Neuser: framework. They are singular, we don't we? We start from from the usual general relativity

355
01:04:25.950 --> 01:04:31.369
Jonas Neuser: black Hole without any modification, so in that sense they are singular. Yes.

356
01:04:33.070 --> 01:04:34.790
Michał Bobula: Okay, thank you for us.

357
01:04:37.340 --> 01:04:40.940
Kristina Giesel: Okay, then, I think it's the point where we

358
01:04:41.450 --> 01:04:58.309
Kristina Giesel: yeah, I can thank all 3 speakers. We don't close the seminar now, but I think it is a good moment to thank all of you for your nice and interesting talks, and also for the discussion that has already taken place. So thanks a lot.

359
01:04:58.930 --> 01:05:11.720
Kristina Giesel: And yeah, we now open the discussion to everybody again. And yeah, are there any questions that people would like to ask the speakers? Or just

360
01:05:12.386 --> 01:05:19.349
Kristina Giesel: to us, to the general audience, or just to comment on things that have been discussed so far.

361
01:05:20.560 --> 01:05:24.578
AAipad2022: I have a quick comment about this, the last point that I just discussed about the

362
01:05:25.070 --> 01:05:29.009
AAipad2022: singularities right? I mean so somewhat surprisingly.

363
01:05:29.430 --> 01:05:34.589
AAipad2022: It is true that in Schwarzschild case, right? I mean, there's this thing central singularity.

364
01:05:35.450 --> 01:05:41.970
AAipad2022: And so if you just take lively quantum fields like the perturbations that were considered in the last talk.

365
01:05:43.720 --> 01:05:56.009
AAipad2022: Then, those perturbations, you know you, you would think that they actually are not well defined, that the the singularity it turns out that although they are not well defined as functions.

366
01:05:56.350 --> 01:06:01.300
AAipad2022: in fact, the operator value distribution corresponding to those

367
01:06:01.790 --> 01:06:13.949
AAipad2022: those correspond to the perturbations that you have got, they actually turn out to be completely well defined as operative value distributions at the singularity.

368
01:06:14.080 --> 01:06:19.919
AAipad2022: and, in fact, the renormalized space energy tensor is also completely well defined at the singularity.

369
01:06:20.240 --> 01:06:22.710
AAipad2022: and therefore, you know, you could

370
01:06:23.350 --> 01:06:33.759
AAipad2022: built, I mean hope to build along the lines of the last talk. Theory, even beyond what I'm saying is that in quantum theory, really.

371
01:06:34.920 --> 01:06:47.259
AAipad2022: we don't care about the functional form of the singularity, for like, if I look at one upon R, for example, in 3 dimensions in Euclidean space, then it's a singular function.

372
01:06:47.610 --> 01:07:12.379
AAipad2022: But in fact, it's a c infinity distribution, because you can take as many derivatives of it. It's it's Laplacian squared will give you a delta distribution, and then you can take further derivatives of it as many as you want. So the main point is that this perturbations would be quite well defined as operator value distributions, and therefore the program that Thomas is pursuing could actually

373
01:07:12.530 --> 01:07:14.520
AAipad2022: proceed without any problem.

374
01:07:19.770 --> 01:07:24.610
Kristina Giesel: And you are buying any further comments.

375
01:07:31.230 --> 01:07:35.069
Western University: Just one question. Maybe if there's 1 more minute.

376
01:07:37.640 --> 01:07:41.113
Western University: This the perturbation you're referring to. It's

377
01:07:42.680 --> 01:07:50.880
Western University: It's not necessarily a perturbation in H bar, right? It's it's dynamical. So it.

378
01:07:51.440 --> 01:07:56.600
Western University: Let me get to the question. There's been an idea floating around a lot that

379
01:07:57.248 --> 01:08:00.479
Western University: some of these bounces. One expect

380
01:08:01.551 --> 01:08:05.609
Western University: have analogies with with tamiling

381
01:08:06.140 --> 01:08:13.699
Western University: in in standard quantum mechanics. Tunneling is one classical trajectory.

382
01:08:13.810 --> 01:08:27.540
Western University: They can jump into another classical trajectory which in the classical theory are not connected, but the quantum theory can jump one for the other. There's a sort of a time independent way of viewing this.

383
01:08:27.720 --> 01:08:48.630
Western University: and but tunneling is a non-analytic in in H bar. Notoriously right. Usually it goes together with some appearances of exponential of one over H bar something which is a standard tunneling formula in elementary. So it's non-perturbative in H bar.

384
01:08:50.220 --> 01:09:05.630
Western University: So I wouldn't expect to capture a quan. A phenomenon similar to to tunneling, including perhaps abounds.

385
01:09:06.140 --> 01:09:16.699
Western University: I mean 1. 1 doesn't get the cosmological bounce by just doing perturbation around a collapsing universe into a singularity when one has to do something else.

386
01:09:18.399 --> 01:09:19.420
Western University: This.

387
01:09:19.670 --> 01:09:28.159
Western University: This is not to say that perturbative technique don't not useful. They're immensely useful.

388
01:09:28.620 --> 01:09:38.100
Western University: But the the non-analyticity of the perhaps in each part of the main phenomena we are considering should be kept in mind. I think.

389
01:09:44.229 --> 01:09:49.109
Kristina Giesel: Thank you, Carlo. There is one more comment or question by Thomas.

390
01:09:53.840 --> 01:09:59.870
thiemann: Yeah. So just to say, yeah. The the perturbation here is in terms of

391
01:10:00.240 --> 01:10:09.080
thiemann: simply a split of the phase space into symmetric and and non-symmetric modes. And

392
01:10:09.190 --> 01:10:15.420
thiemann: then you expand. It's basically a tailor expansion of the expression that you're interested in.

393
01:10:15.830 --> 01:10:22.420
thiemann: And once you have that to your desired order of accuracy. You can

394
01:10:22.530 --> 01:10:26.649
thiemann: turn on the quantum mechanical questions that you're asking.

395
01:10:27.010 --> 01:10:32.430
thiemann: One of them would be if there's something like tunneling, and the tunneling formula

396
01:10:32.570 --> 01:10:43.700
thiemann: is, in a sense derived from the Schrodinger, the linear Schrodinger equation. And of course it's non-alytic in in H bar, one over in in H bar.

397
01:10:43.820 --> 01:10:49.530
thiemann: and something like that could happen here also that has nothing to do with the perturbation theory.

398
01:10:50.770 --> 01:10:55.370
Western University: Yeah, yeah, I see this. Yeah, thanks.

399
01:10:55.990 --> 01:10:56.540
thiemann: Sure.

400
01:10:58.100 --> 01:11:04.019
Kristina Giesel: Okay, thank you, Thomas. There is one more hand raised by Hassan. So please go ahead.

401
01:11:04.430 --> 01:11:29.379
Hassan Mehmood: Yeah, I just wanted to make a quick comment about a question that Jonas asked to Francesco about the existence of shell crossings beyond spherical symmetry. There are 2 comments. Firstly, we can generalize the definition of a shell crossing singularity beyond spherical symmetry. It has been done in the literature. Secondly, you can use that more generalized definition

402
01:11:29.380 --> 01:11:39.310
Hassan Mehmood: to test for the existence of shell crossings just in the classical theory. It can be very concretely done in, for instance, 3D. Gravity.

403
01:11:39.310 --> 01:11:53.550
Hassan Mehmood: And it turns out in the classical theory. Suppose if you take a fluid and provided that it is only irrational, you can show that there are shell crossings, and they exist quite generally for quite a large class of initial data.

404
01:11:54.310 --> 01:12:04.770
Hassan Mehmood: So I mean, I expect I agree with Francesco that even in the effective theory. If we were to go beyond spherical symmetry, shell crossings should persist.

405
01:12:05.290 --> 01:12:08.550
Hassan Mehmood: If we are considering a fluid that's irrational.

406
01:12:14.320 --> 01:12:16.195
Kristina Giesel: Thank you. Hassan.

407
01:12:17.310 --> 01:12:19.670
Kristina Giesel: Any more comments, questions.

408
01:12:20.170 --> 01:12:23.989
AAipad2022: Yeah, a quick question for Thomas, I mean. So, Thomas, in in your

409
01:12:24.190 --> 01:12:27.709
AAipad2022: program that we just mentioned in reply to Carlos, comment,

410
01:12:29.820 --> 01:12:35.939
AAipad2022: are you not considering for quantization, for this inhomogeneous modes, or for these non spherical modes.

411
01:12:38.950 --> 01:12:41.259
thiemann: At the moment. Yeah, we are considering.

412
01:12:41.260 --> 01:12:46.170
AAipad2022: Right. So I think that so I think one would. So the bounce could occur from the

413
01:12:46.720 --> 01:12:50.690
AAipad2022: some something non-trivial happening in the spherical symmetric sector already.

414
01:12:51.710 --> 01:12:56.400
AAipad2022: and but I think the fog quantization would not really contribute to that bounce.

415
01:12:57.910 --> 01:13:09.713
AAipad2022: The the non-symmetric modes, the non spherically symmetric modes would not unlikely to me. It it yeah,

416
01:13:10.950 --> 01:13:14.099
AAipad2022: you, you need something to me, at least it would seem that.

417
01:13:14.630 --> 01:13:21.700
AAipad2022: But, on the other hand, I think for the sets the spherical symmetric modes you're not using. You're using Lqg, and you're using quantum geometries only.

418
01:13:21.860 --> 01:13:27.930
AAipad2022: And there I think that could give rise to the bounce that you you are mentioning is is due.

419
01:13:28.250 --> 01:13:29.390
AAipad2022: Agree with this.

420
01:13:29.710 --> 01:13:40.480
thiemann: Yeah, so so it's a little bit like the following idea, yeah, you're always struggling with the immense non-linearity of of gravity.

421
01:13:40.740 --> 01:13:46.660
thiemann: And in this decomposition of the phase space into symmetric and non-symmetric modes.

422
01:13:48.120 --> 01:13:57.560
thiemann: The the idea is to treat the the symmetric modes in their full nonlinearity, using using the Lq. Methods and the other stuff.

423
01:13:57.830 --> 01:14:00.610
thiemann: It's a little bit like in the Hybrid Cosmology picture.

424
01:14:01.110 --> 01:14:06.029
AAipad2022: Right? Exactly. So that I think is yeah, that that I agree and understand. Thank you.

425
01:14:06.450 --> 01:14:07.010
thiemann: Sure.

426
01:14:12.540 --> 01:14:15.962
Kristina Giesel: Okay, thank you very much. Thomas and Abbai.

427
01:14:17.410 --> 01:14:22.059
Kristina Giesel: at the moment I don't see any further questions.

428
01:14:23.970 --> 01:14:32.110
Kristina Giesel: So yeah, then let me thank again all speakers and all the entire audience for participating.

429
01:14:33.040 --> 01:15:01.310
Kristina Giesel: I really enjoyed this symposium also. Thank you very much to the Organizing Committee to suggest these kind of formats. It was also wonderful to see our young researchers acting in this symposium and giving these nice and excellent talks. So thank you very much. And yeah, the next international quantum gravity seminar will be in 2 weeks. And yeah, we are looking forward to see everybody there again.

430
01:15:03.080 --> 01:15:07.700
Hal Haggard: Thanks also to Christina for hosting today. Thank you so much, Christina.

431
01:15:07.850 --> 01:15:18.099
Hal Haggard: In 2 weeks we have Philip Owen. He's speaking on gravitational algebras entropy and quantum reference frames. Hope to see you there. Thank you. Everyone.

432
01:15:19.120 --> 01:15:20.109
Kristina Giesel: I'm sure I look.