0 00:00:02,610 --> 00:00:09,000 Jorge Pullin: Okay, sorry speaker to this much your subscale who will speak about Korean at the center space times that admit non singular horizons. 1 00:00:11,519 --> 00:00:13,830 Warsaw LQG: Okay. Hello and welcome. 2 00:00:15,059 --> 00:00:24,810 Warsaw LQG: So this is actually a joint work of mine with Priscilla on those key that we're doing here and the faculty of physics at the University for so and 3 00:00:27,270 --> 00:00:42,510 Warsaw LQG: What I want to talk today about at the first the Colonel's and the disk space times they are not the most commonly and contact space dance one considers in GR so to me. 4 00:00:43,740 --> 00:00:46,140 Warsaw LQG: Until I break down some of their properties. 5 00:00:48,180 --> 00:00:48,690 Warsaw LQG: Then 6 00:00:50,010 --> 00:00:52,680 Warsaw LQG: I will introduce the conditions. 7 00:00:54,600 --> 00:01:01,800 Warsaw LQG: Conditions for the removal of the singularity of the clinical singularity of the horizons in the cabinet and the space times 8 00:01:04,260 --> 00:01:08,340 Warsaw LQG: Some discussion about what are those singularities. 9 00:01:10,080 --> 00:01:10,440 Warsaw LQG: And 10 00:01:11,610 --> 00:01:23,340 Warsaw LQG: What is quite surprising result in the same conditions for the removing of singularity and the singularity, the horizon can be extended to the neighborhoods. 11 00:01:24,660 --> 00:01:32,340 Warsaw LQG: Of the non singular horizon. So that will be the next point I will talk about. And finally, 12 00:01:34,680 --> 00:01:36,120 Warsaw LQG: Our work is connected 13 00:01:38,310 --> 00:01:53,070 Warsaw LQG: To another topic. Our team is working on so connected to the type the horizons on the non trivial fiber abundance of our sphere, and I will show some connection of our long singular horizon to this work. 14 00:01:55,410 --> 00:02:03,030 Warsaw LQG: As well as some generalization of our results extending to the accelerator cannot see the space times 15 00:02:04,650 --> 00:02:09,450 Warsaw LQG: In this case, even, can I think the Secret Space Time accelerated, of course. 16 00:02:13,680 --> 00:02:18,360 Warsaw LQG: So what are the seeds are planted the seed stage names. 17 00:02:19,530 --> 00:02:30,120 Warsaw LQG: There are solutions to the vacuum Einstein equations with cosmological constant. And it's a four dimensional family parameter is by 18 00:02:31,710 --> 00:02:44,010 Warsaw LQG: For real numbers, usually, usually interpreted as the muscle my call as the curl parameter connected to the angular momentum of the black hole. 19 00:02:45,930 --> 00:02:50,970 Warsaw LQG: Just like home is on the cosmological constant background. 20 00:02:53,340 --> 00:02:55,350 Warsaw LQG: For the sign is 21 00:02:57,330 --> 00:03:09,000 Warsaw LQG: A sprig can be positive, negative, and there's this one quite exotic parameter called and they're not parameter first discovered in the top not 22 00:03:10,560 --> 00:03:13,980 Warsaw LQG: Space, which was the extension of fortunes swatches. 23 00:03:16,200 --> 00:03:16,950 Warsaw LQG: Black Hole. 24 00:03:17,970 --> 00:03:21,840 Warsaw LQG: And introduction and is not parameter means for us. 25 00:03:24,000 --> 00:03:27,210 Warsaw LQG: Some, some new to political 26 00:03:29,220 --> 00:03:31,770 Warsaw LQG: Considerations has to be taken into account. 27 00:03:35,100 --> 00:03:35,610 Warsaw LQG: So, 28 00:03:37,080 --> 00:03:41,790 Warsaw LQG: Before I begin, I want to talk about some motivation for our work. 29 00:03:43,110 --> 00:03:43,680 Warsaw LQG: So, 30 00:03:46,830 --> 00:03:49,830 Warsaw LQG: The person wanted to investigate just the 31 00:03:51,840 --> 00:03:55,050 Warsaw LQG: The horizons of the current not the Sitter space times 32 00:03:56,700 --> 00:04:10,470 Warsaw LQG: Because you know 13 there was there was some results concerning the solutions to the pit of the equations, which provides us with the geometry of the isolated horizons of time thing. 33 00:04:15,150 --> 00:04:27,000 Warsaw LQG: Any particular one recent ones and paper by the mosquito cleverness garage discusses the family of type the horizons of the topology bundle. 34 00:04:29,040 --> 00:04:29,400 Warsaw LQG: Which 35 00:04:32,880 --> 00:04:40,500 Warsaw LQG: When you, when you pose the vacuum is the equations and provided by industry that I selected horizon solutions. 36 00:04:41,640 --> 00:04:47,610 Warsaw LQG: And those solutions are actually privatized by four parameters so 37 00:04:49,200 --> 00:05:00,270 Warsaw LQG: We conjecture that probably those horizons should be some relation to the current not until they see their space times because the as well and four dimensional family. 38 00:05:01,860 --> 00:05:05,940 Warsaw LQG: But as we discovered later this, the decision was 39 00:05:07,530 --> 00:05:09,510 Warsaw LQG: Quite less obvious than we expected. 40 00:05:10,710 --> 00:05:15,480 Warsaw LQG: So I'm expecting some results only on the sub family of Colonel 41 00:05:16,530 --> 00:05:20,640 Warsaw LQG: colonel colonel this space, things are on the family. 42 00:05:21,750 --> 00:05:25,860 Warsaw LQG: Of the four dimensional family of time the horizons. 43 00:05:29,010 --> 00:05:31,830 Warsaw LQG: So this is the general form of the 44 00:05:33,360 --> 00:05:38,760 Warsaw LQG: Current not under the sitter metric and 45 00:05:44,460 --> 00:05:45,330 Warsaw LQG: There are some 46 00:05:46,950 --> 00:05:53,580 Warsaw LQG: Some things, one should maybe understand just by looking at this metric. So first thing that 47 00:05:54,990 --> 00:06:07,230 Warsaw LQG: It can be seen. That's just a generalization of the previously known like how solutions. So for the for the not parameter equals zero, we will cover the 48 00:06:08,310 --> 00:06:10,200 Warsaw LQG: I think this either spacetime. 49 00:06:12,420 --> 00:06:13,200 Warsaw LQG: And for 50 00:06:14,820 --> 00:06:21,540 Warsaw LQG: A equal to zero and lambda equal to zero. So we actually covered the original thousand ounce metric 51 00:06:22,890 --> 00:06:25,290 Warsaw LQG: So there are a couple of 52 00:06:26,730 --> 00:06:30,810 Warsaw LQG: Things that are quite suspicious. Like, for example, 53 00:06:33,750 --> 00:06:41,850 Warsaw LQG: There are places in the world where we divide in that component, the component of metric so 54 00:06:42,900 --> 00:06:53,940 Warsaw LQG: And my assumption the function P which appears in the beta coefficient has to be has to be positive. It also guarantees us that the 55 00:06:55,440 --> 00:07:00,270 Warsaw LQG: Them signature is Lawrence young so we use, minus, plus, plus, plus. 56 00:07:03,990 --> 00:07:14,340 Warsaw LQG: On the other hand, we also divided by the function kill and dysfunction, kill, as we said later so is corresponding to the 57 00:07:16,830 --> 00:07:19,830 Warsaw LQG: To the kidney crisis on the cabinet. 58 00:07:23,370 --> 00:07:24,120 Warsaw LQG: Space times 59 00:07:29,370 --> 00:07:33,450 Warsaw LQG: Yes. And what's also important about this metric that 60 00:07:34,500 --> 00:07:44,070 Warsaw LQG: As all of the Type D solutions we have algebra have any factors spammed by to committing deals. So we have 61 00:07:45,120 --> 00:07:48,720 Warsaw LQG: The opportunity which is time translation symmetry. 62 00:07:50,670 --> 00:08:01,710 Warsaw LQG: And also the over the five, which means for us that this metric is as a rotational symmetry. 63 00:08:08,730 --> 00:08:09,360 Warsaw LQG: Yes, so 64 00:08:11,490 --> 00:08:14,400 Warsaw LQG: They want to discuss the clinical singularity. 65 00:08:16,950 --> 00:08:26,880 Warsaw LQG: Which stems from the fact that when we, when you consider this one form a defy which appeared 66 00:08:29,250 --> 00:08:33,210 Warsaw LQG: Appeared in the time like metric component 67 00:08:35,850 --> 00:08:37,020 Warsaw LQG: They discovered that 68 00:08:38,250 --> 00:08:41,940 Warsaw LQG: If the L is not zero. So when we have some not parameter 69 00:08:43,350 --> 00:08:58,170 Warsaw LQG: This one phone does not doesn't punish at the pole data equals the pie. So this means for us that the G is not continuous, and the whole semi access Sita equal to buy 70 00:08:59,430 --> 00:09:13,410 Warsaw LQG: And obviously this is a coordinate and dependent statement. So one could choose another coordinate and accordingly transform this singular access. So for example, if you introduce 71 00:09:15,990 --> 00:09:19,920 Warsaw LQG: The prime which is T minus four L fi then 72 00:09:21,060 --> 00:09:23,910 Warsaw LQG: Our one phone transfers and 73 00:09:25,050 --> 00:09:25,740 Warsaw LQG: Such that 74 00:09:26,760 --> 00:09:30,690 Warsaw LQG: It then becomes a prime the data and then 75 00:09:31,770 --> 00:09:34,530 Warsaw LQG: And discussing squared is for us that 76 00:09:35,820 --> 00:09:42,810 Warsaw LQG: This one doesn't management and the semi access data at 1.0 and the genius not continues and 77 00:09:44,310 --> 00:10:00,090 Warsaw LQG: At the at the other similar axes of course for any other choice of the of the team coordinators, for example, and TVs equals t minus two, five should be to find 78 00:10:03,090 --> 00:10:09,600 Warsaw LQG: This one from doesn't punch that the balls balls and the jury is not continuous. In the whole access so 79 00:10:11,370 --> 00:10:18,870 Warsaw LQG: One of our refers to this space times as having the gravitational magnetic monopole while 80 00:10:22,050 --> 00:10:25,140 Warsaw LQG: When this singular axes corresponds to the 81 00:10:26,250 --> 00:10:35,070 Warsaw LQG: To the Mr string connecting the magnetic the bone and as was in that case, we could 82 00:10:36,900 --> 00:10:45,210 Warsaw LQG: Talk about the gravitational magnetic monopole one could choose engage such thoughts, want to switch which access is singular. 83 00:10:46,320 --> 00:10:46,770 Warsaw LQG: And 84 00:10:47,880 --> 00:11:00,450 Warsaw LQG: For the generic values of parameters. So of the mass exposure constant current not parameters the space time you singular in at least one poll 85 00:11:01,860 --> 00:11:03,840 Warsaw LQG: And usually, usually above us. 86 00:11:07,410 --> 00:11:13,710 Warsaw LQG: So there was some propositions in how to remediate those problems. 87 00:11:14,910 --> 00:11:16,350 Warsaw LQG: For example, for example. 88 00:11:17,820 --> 00:11:19,590 Warsaw LQG: Mr considered 89 00:11:20,820 --> 00:11:27,780 Warsaw LQG: Originally I thought not space. So a limit of without care parameter AND CHRIS MITCHELL constant 90 00:11:29,160 --> 00:11:30,210 Warsaw LQG: When we could take 91 00:11:32,610 --> 00:11:40,110 Warsaw LQG: Don't know senior solutions. So one with the singular axis at the southern hemisphere and one and the 92 00:11:41,340 --> 00:11:51,120 Warsaw LQG: Senior axis and the Northern Hemisphere and then we take from the, from the left one. The know them not singular hemisphere and glue it to the 93 00:11:52,320 --> 00:11:52,980 Warsaw LQG: Southern 94 00:11:54,060 --> 00:11:54,840 Warsaw LQG: Of the right 95 00:11:56,520 --> 00:11:57,420 Warsaw LQG: Space and 96 00:11:58,980 --> 00:12:00,720 Warsaw LQG: In this way we arrived at the 97 00:12:02,460 --> 00:12:06,330 Warsaw LQG: At the top, not space time which is which is not senior 98 00:12:07,530 --> 00:12:13,200 Warsaw LQG: At the slides, the slides cost of having a periodic to coordinate 99 00:12:16,230 --> 00:12:24,540 Warsaw LQG: And then the resulting topology is a free spirit times, times around this topic, not space. So our results. 100 00:12:25,560 --> 00:12:28,470 Warsaw LQG: And remained results states that this is not enough. 101 00:12:29,610 --> 00:12:34,890 Warsaw LQG: In the general case in the generic case of digital space times so 102 00:12:36,000 --> 00:12:42,060 Warsaw LQG: One can one can make is doing in the arbitrary case. But then one discovers that 103 00:12:44,370 --> 00:12:45,300 Warsaw LQG: We don't have this 104 00:12:46,830 --> 00:12:57,480 Warsaw LQG: Resulting topology of US frame and our glowing is such that the horizon that the holes are still not differentiable 105 00:12:58,740 --> 00:13:00,270 Warsaw LQG: So what we discovered 106 00:13:01,350 --> 00:13:04,860 Warsaw LQG: Is that the glowing is differentiable 107 00:13:06,300 --> 00:13:23,490 Warsaw LQG: And in fact we by investigation explicitly check that at least twice differentiable, only if this is condition is satisfied. So if we overlap that was to a squared r squared plus two r zero squared. 108 00:13:24,780 --> 00:13:28,320 Warsaw LQG: Where r zero is a radius of 109 00:13:29,490 --> 00:13:30,150 Warsaw LQG: Have a 110 00:13:31,650 --> 00:13:35,490 Warsaw LQG: Clinic Christ on which we want to make non singular 111 00:13:39,840 --> 00:13:44,820 Warsaw LQG: So a couple, a couple of words about the current the sitter horizons. 112 00:13:46,050 --> 00:13:50,190 Warsaw LQG: So, as I told you before the horizons are 113 00:13:52,530 --> 00:13:56,400 Warsaw LQG: Correspond to the to the zeros of this Q function. 114 00:13:57,540 --> 00:14:09,420 Warsaw LQG: Actually just a polynomial polynomial in in the coordinates are so it's for for the recording recording phenomenal so 115 00:14:11,460 --> 00:14:16,230 Warsaw LQG: We have up to four killing horizons and one can check that. 116 00:14:17,250 --> 00:14:34,620 Warsaw LQG: In fact surfaces of our he was to our CEO and our surface surfaces and they are crayons and their clinic horizons never buy this Kinney vector side which we use extensively in this 117 00:14:35,730 --> 00:14:37,860 Warsaw LQG: In our research paper. 118 00:14:42,270 --> 00:14:48,090 Warsaw LQG: Which is just a just a certain linear combination of the two factors that we 119 00:14:49,140 --> 00:14:53,670 Warsaw LQG: That we have. And maybe one important thing to notice. 120 00:14:54,870 --> 00:14:55,620 Warsaw LQG: Is that 121 00:14:58,050 --> 00:14:58,830 Warsaw LQG: Is that 122 00:15:01,830 --> 00:15:02,160 Warsaw LQG: This 123 00:15:03,210 --> 00:15:04,260 Warsaw LQG: Killing vector field. 124 00:15:05,550 --> 00:15:08,100 Warsaw LQG: Explicitly depends on the right is on the horizon. 125 00:15:14,190 --> 00:15:14,580 Yes. 126 00:15:17,460 --> 00:15:18,000 Warsaw LQG: So, 127 00:15:19,020 --> 00:15:24,570 Warsaw LQG: Actually, the, the original metric and the original form the metric that I showed 128 00:15:26,460 --> 00:15:32,400 Warsaw LQG: Was singular at the at the horizon. So, one cannot use it to describe the 129 00:15:33,510 --> 00:15:46,830 Warsaw LQG: The Christ and geometry. But what we can do is we can introduce the slightly change call frame. So this coordinate be is an analog over 130 00:15:49,320 --> 00:15:50,580 Warsaw LQG: Of an advanced time 131 00:15:51,600 --> 00:15:55,290 Warsaw LQG: And actually, it just reduces to the advanced time for 132 00:15:56,430 --> 00:15:57,780 Warsaw LQG: For the suitcase. 133 00:15:59,310 --> 00:16:05,550 Warsaw LQG: And also to introduce some some twisted and twisted ankle coordinate 134 00:16:10,470 --> 00:16:16,320 Warsaw LQG: Which is not, not necessarily in the into taking cases we have here and a 135 00:16:17,850 --> 00:16:18,360 Warsaw LQG: And then 136 00:16:20,010 --> 00:16:28,320 Warsaw LQG: You can you can calculate the there's nothing metric that is announcing that are at the horizon. So as you can see 137 00:16:29,580 --> 00:16:31,680 Warsaw LQG: This this troublesome. 138 00:16:32,910 --> 00:16:45,690 Warsaw LQG: Factor of one overkill, which was connected to them the r squared coordinate is no longer appears so our, our metric is is totally fine. And the horizon. 139 00:16:47,010 --> 00:16:51,780 Warsaw LQG: And here we explicitly say that the surfaces. 140 00:16:53,280 --> 00:16:53,970 Warsaw LQG: Of 141 00:16:55,500 --> 00:16:58,800 Warsaw LQG: Constant. Constant. Constant radius. 142 00:17:00,390 --> 00:17:01,830 Warsaw LQG: R zero 143 00:17:03,420 --> 00:17:05,820 Warsaw LQG: Gives us the agenda metric 144 00:17:07,680 --> 00:17:08,820 Warsaw LQG: On the horizon. 145 00:17:12,870 --> 00:17:19,980 Warsaw LQG: And those sigma zero functions and roles, your functions are just the previous functions introduced 146 00:17:21,210 --> 00:17:23,490 Warsaw LQG: With the metric components. 147 00:17:25,110 --> 00:17:26,970 Warsaw LQG: But for the horizon. 148 00:17:28,050 --> 00:17:28,590 Warsaw LQG: Ranges. 149 00:17:33,810 --> 00:17:36,690 Warsaw LQG: So we want to want to introduce 150 00:17:39,600 --> 00:17:42,990 Warsaw LQG: You coordinates on this singular horizon. 151 00:17:47,820 --> 00:17:48,180 Warsaw LQG: And 152 00:17:49,680 --> 00:17:56,640 Warsaw LQG: In fact, this coordinates expo and x ray are the coordinates on the space of now generators of the horizon. 153 00:17:57,930 --> 00:17:58,290 Warsaw LQG: And 154 00:17:59,880 --> 00:18:03,600 Warsaw LQG: When completed with this coordinate style those coordinates. 155 00:18:05,340 --> 00:18:09,780 Warsaw LQG: We just need coordinate systems on the on the horizon and 156 00:18:11,730 --> 00:18:13,140 Warsaw LQG: Great vibe from this curtness 157 00:18:17,700 --> 00:18:20,970 Warsaw LQG: That they are somewhat perpendicular to the 158 00:18:23,430 --> 00:18:24,780 Warsaw LQG: Today, killing better 159 00:18:25,800 --> 00:18:29,280 Warsaw LQG: So, so the size of X to an extra 160 00:18:30,450 --> 00:18:30,960 Warsaw LQG: Damage 161 00:18:34,200 --> 00:18:36,840 Warsaw LQG: So make a particular choice. 162 00:18:37,860 --> 00:18:39,240 Warsaw LQG: Of the talk. Responding to 163 00:18:40,710 --> 00:18:41,610 Warsaw LQG: To be and 164 00:18:42,990 --> 00:18:49,380 Warsaw LQG: X to tune the data and expect to some some combination of the and 165 00:18:51,390 --> 00:18:55,080 Warsaw LQG: And fight to the connected with 166 00:18:56,460 --> 00:19:00,420 Warsaw LQG: Collectors also to this Amiga which define the 167 00:19:02,310 --> 00:19:03,960 Warsaw LQG: The killing machine vector 168 00:19:09,210 --> 00:19:10,920 Warsaw LQG: And then we have this 169 00:19:12,120 --> 00:19:12,990 Warsaw LQG: This new 170 00:19:14,220 --> 00:19:24,240 Warsaw LQG: Horizon metric in this new ordinance when what it is even. It's even easier to see that he said that Jeanette degenerate metric on them on the horizon. 171 00:19:27,690 --> 00:19:30,270 Warsaw LQG: And one thing I should also point out is that 172 00:19:31,680 --> 00:19:34,350 Warsaw LQG: Will probably use this fact that 173 00:19:36,660 --> 00:19:40,410 Warsaw LQG: In this in this coordinate the tower is just side. 174 00:19:41,520 --> 00:19:44,190 Warsaw LQG: So it will simplify some some notation. 175 00:19:48,780 --> 00:19:49,500 Warsaw LQG: Yes, and 176 00:19:50,730 --> 00:19:54,360 Warsaw LQG: Maybe some intuitions about once or this clinical singularity. 177 00:19:55,380 --> 00:20:10,260 Warsaw LQG: And responsible, so we can we can consider section of their horizon and in many cases, one one expect this section of the horizon to have the topology of the spear. 178 00:20:11,400 --> 00:20:16,350 Warsaw LQG: But there might be some some problems in the Pops. 179 00:20:17,430 --> 00:20:19,650 Warsaw LQG: In fact, our, our previous metric 180 00:20:21,240 --> 00:20:22,620 Warsaw LQG: Was analytic everywhere. 181 00:20:23,850 --> 00:20:32,550 Warsaw LQG: Except for me from the, from the post. So, so what I want to survey to study this metric. The only suspicious points are 182 00:20:34,830 --> 00:20:53,490 FAU Erlangen: Me. Can I make a comment is, so actually this figure, which is the next slide. It is the it's not a slice of the horizon. It is the projected space. This is the space of the knowledge generators and this is exactly this metric from the previous slide. 183 00:20:56,460 --> 00:20:57,000 Warsaw LQG: Yes, yes. 184 00:21:03,090 --> 00:21:11,490 Warsaw LQG: So what can go wrong in the polls, is that we, we can have some kind of some kind of wedge this this web this 185 00:21:13,140 --> 00:21:18,510 Warsaw LQG: Corresponds to this clinical singularity. And one way of saying it is 186 00:21:20,610 --> 00:21:25,890 Warsaw LQG: Is that we simply chose chose the range of the angular Coordinates. Coordinates wrong. 187 00:21:27,480 --> 00:21:27,930 Warsaw LQG: And 188 00:21:30,540 --> 00:21:34,950 Warsaw LQG: I would like their methods is based on considering and such loops. 189 00:21:35,970 --> 00:21:36,420 Warsaw LQG: Around 190 00:21:38,490 --> 00:21:44,610 Warsaw LQG: Circles circles around the symmetry access and in the case of the 191 00:21:47,400 --> 00:21:59,190 Warsaw LQG: Way from far from the pole, this, this ratio should obviously be to buy, but there might be some problems in the post. And then we'd like to impose the conditions. 192 00:22:01,140 --> 00:22:06,300 Warsaw LQG: That duration of circumference to the radius in the post will also be 193 00:22:07,860 --> 00:22:09,300 Warsaw LQG: Like on the to secure. So to buy 194 00:22:11,010 --> 00:22:23,250 Warsaw LQG: Yeah, so that's exactly. That's exactly what I'm going to talk now. So, so far we haven't made many assumptions about the the nature of the coordinates x to an extreme. And in fact, 195 00:22:24,720 --> 00:22:27,570 Warsaw LQG: In fact, we didn't assume that there are spiritual coordinates. 196 00:22:29,370 --> 00:22:31,170 Warsaw LQG: So explain 197 00:22:33,150 --> 00:22:33,720 Warsaw LQG: Expands 198 00:22:34,950 --> 00:22:48,870 Warsaw LQG: expands on some interval close at the one side, which is two pi time. See, and later on finding this the suitable see constant will allow us to remove that 199 00:22:49,950 --> 00:22:51,060 Warsaw LQG: The single the 200 00:22:52,350 --> 00:22:53,610 Warsaw LQG: Clinical singularity. 201 00:22:56,730 --> 00:22:57,300 Warsaw LQG: So, 202 00:23:03,810 --> 00:23:17,280 Warsaw LQG: So actually made a little bit of assumptions that, but there may be not assumptions, because they can be seen from the, from the form of the metric that x to y equals zero corresponds to the single bond and 203 00:23:18,720 --> 00:23:26,370 Warsaw LQG: So our poll is a single point, and I still equals to some other concerns our circles on this. 204 00:23:27,540 --> 00:23:29,220 Warsaw LQG: Space of no generators 205 00:23:30,540 --> 00:23:32,730 Warsaw LQG: Now we have to define 206 00:23:34,380 --> 00:23:39,750 Warsaw LQG: Went to consider the circles of a constant stone and define for them. 207 00:23:40,950 --> 00:23:44,700 Warsaw LQG: There's a conference which is an integral of the 208 00:23:47,310 --> 00:23:48,660 Warsaw LQG: Of the of the components. 209 00:23:49,770 --> 00:23:51,630 Warsaw LQG: And thank you, free free 210 00:23:54,090 --> 00:24:08,250 Warsaw LQG: Along the circle and then we want to introduce the radius which we calculate in such a in different ways in different calls different polls and this choice is made so that 211 00:24:10,230 --> 00:24:13,440 Warsaw LQG: So that the radius calculated along this 212 00:24:14,460 --> 00:24:15,180 Warsaw LQG: And this 213 00:24:16,830 --> 00:24:19,860 Warsaw LQG: Money for that. You want some beautiful 214 00:24:20,910 --> 00:24:26,940 Warsaw LQG: Spirit is calculated along along just disappear and 215 00:24:30,210 --> 00:24:31,470 Warsaw LQG: The radius on the northern 216 00:24:32,550 --> 00:24:33,240 Warsaw LQG: Hemisphere. 217 00:24:34,980 --> 00:24:46,410 Warsaw LQG: should train to zero as we approach the pole and the same goes for the rate is defined the southern hemisphere. So it should also shrink to zero when we approach approach the boss. 218 00:24:52,050 --> 00:24:55,800 Warsaw LQG: So as I mentioned earlier, our condition. 219 00:24:57,450 --> 00:25:03,480 Warsaw LQG: Our condition that the radius that the ratio of the circumference to the radius. 220 00:25:05,040 --> 00:25:16,140 Warsaw LQG: Has to be checked in, in the suspicious points of our metrics on the pose and they simply corresponds to taking the limits of the circumference and their ideas. 221 00:25:17,190 --> 00:25:19,230 Warsaw LQG: In boats boats and 222 00:25:21,780 --> 00:25:27,570 Warsaw LQG: Making strength of this limit has to be to buy so that we will cover the result from a sphere. 223 00:25:32,010 --> 00:25:34,560 Warsaw LQG: And so because in the in the integration. 224 00:25:37,980 --> 00:25:51,540 Warsaw LQG: Interval appears. This is Kelly constancy. And he says, he says the the condition on this is getting constant. So for the. So the first thing is that we want. 225 00:25:52,830 --> 00:26:14,280 Warsaw LQG: That we want this rescaling constant to be to be the same in both balls, so that's that's what this first equations equations stems from and then we see that there's Kelly constantly simply one over the, over zero so that we have to fight for example in in this in this Poland. 226 00:26:15,720 --> 00:26:17,940 Warsaw LQG: If this part satisfies 227 00:26:19,530 --> 00:26:21,810 Warsaw LQG: The first constraint and we also had 228 00:26:23,460 --> 00:26:31,860 Warsaw LQG: To to find and the brief reminder about dysfunction be so in general this condition this condition. 229 00:26:33,780 --> 00:26:40,620 Warsaw LQG: Should depends on the on all of the parameters of the Colonel's and the Sitter space time. So we have 230 00:26:42,900 --> 00:26:44,670 Warsaw LQG: Except from like from them. So 231 00:26:46,260 --> 00:26:48,660 Warsaw LQG: So we have great news. Not parameter 232 00:26:50,550 --> 00:26:53,940 Warsaw LQG: Awesome. Sure appears because mariska constant 233 00:26:56,520 --> 00:27:03,690 Warsaw LQG: So in five our, our constraint is quite with the study because we will cover the previously known. 234 00:27:06,360 --> 00:27:27,150 Warsaw LQG: This no solutions which are which do admit Monsignor our horizons. So first, if one says, because much constant to zero then then be PLC one piece of pie are equal. And then the only choice to make this distraction. One is to 235 00:27:28,260 --> 00:27:40,560 Warsaw LQG: Either have l equal to zero and so that the squad takes care of the miners or have a equal to zero. And those corresponds to either current or 12 not 236 00:27:41,880 --> 00:27:42,600 Warsaw LQG: Space times 237 00:27:44,520 --> 00:27:45,330 Warsaw LQG: Similarly, 238 00:27:47,550 --> 00:27:48,840 Warsaw LQG: Similarly, if one 239 00:27:49,860 --> 00:27:51,270 Warsaw LQG: Takes equal to zero. 240 00:27:52,350 --> 00:27:55,200 Warsaw LQG: So some curve and visitors FaceTime or 241 00:27:57,390 --> 00:28:04,470 Warsaw LQG: Equal to zero and some some London so told not to disturb space time. Then we also have 242 00:28:05,490 --> 00:28:12,480 Warsaw LQG: Feels very well be of bison, so it's good that our, our constraint recovers the non non singular solutions. 243 00:28:14,310 --> 00:28:18,300 Warsaw LQG: But there's one more choice. One more solution to this equation. 244 00:28:19,530 --> 00:28:25,440 Warsaw LQG: And this distortion requires a couple of assumptions. So it requires that all of the 245 00:28:27,120 --> 00:28:31,050 Warsaw LQG: All of the parameters are non zero so 246 00:28:35,100 --> 00:28:40,560 Warsaw LQG: So, so, in particular, we cannot have any symptoms are 247 00:28:42,450 --> 00:28:45,750 Warsaw LQG: Not solution without customers are constant 248 00:28:46,980 --> 00:28:53,580 Warsaw LQG: And this is this is the constraint. I was, I was thinking earlier and it might be also 249 00:28:56,190 --> 00:29:06,660 Warsaw LQG: Intuitive to see why why it doesn't admit zero because Mitchell, a constant because we we actually, when do I mean the rescaling constant, we, we did. Bye bye. Bye. 250 00:29:11,250 --> 00:29:18,300 Warsaw LQG: Then our, our constraints has are zero and we like to probably would rather 251 00:29:20,640 --> 00:29:25,320 Warsaw LQG: Maybe not in general the the space time is prioritized by Master 252 00:29:26,460 --> 00:29:27,690 Warsaw LQG: actually solving solving 253 00:29:30,000 --> 00:29:40,110 Warsaw LQG: We can solve and the queue of our zero equals zero and get and get the, the mass of the black hole. 254 00:29:44,010 --> 00:29:50,490 Warsaw LQG: So a couple of remarks about the geometry of the space of the now geneticists decry some 255 00:29:53,010 --> 00:29:53,850 Warsaw LQG: Some now. 256 00:29:54,960 --> 00:29:55,950 Warsaw LQG: Now the coordinates. 257 00:30:00,780 --> 00:30:02,430 Warsaw LQG: X two X extreme 258 00:30:05,370 --> 00:30:14,940 Warsaw LQG: Has this range, when we determined determined the rescaling constant is one over P of zero and one could really nicely. 259 00:30:16,110 --> 00:30:24,480 Warsaw LQG: describe those those horizons, because we can explicitly calculate the value of the other area so 260 00:30:26,520 --> 00:30:33,690 Warsaw LQG: It's somewhat connected to the reason why we cannot have a negative customer Chad constant 261 00:30:34,860 --> 00:30:43,110 Warsaw LQG: Because as long can see then the area would be negative. And in fact, the this condition for lambda 262 00:30:45,750 --> 00:31:00,210 Warsaw LQG: Complaints only, only some positive numbers and then the squares of the parameters. So, so we have no no singular bicker not emptying the Sitter space times with 263 00:31:02,430 --> 00:31:04,620 Warsaw LQG: With customers with negative because much a constant. 264 00:31:05,910 --> 00:31:06,450 Warsaw LQG: So, 265 00:31:07,680 --> 00:31:19,770 Warsaw LQG: We explicitly check that. Our philosophy is at least twice differentiable at the polls. So, so that the metric that the components of the metric or at least twice in different ways differentiable 266 00:31:21,720 --> 00:31:25,470 Warsaw LQG: But contrary to the for example current horizons. 267 00:31:26,550 --> 00:31:28,170 Warsaw LQG: They do not have 268 00:31:29,550 --> 00:31:38,970 Warsaw LQG: The topology over to spear times, times our. So actually, our horizons have some of the apology have some non trivial. 269 00:31:40,170 --> 00:31:45,030 Warsaw LQG: Fiber been over a stone, such as such as, for example, hope bundle. 270 00:31:46,500 --> 00:31:48,420 Warsaw LQG: And there is also some 271 00:31:49,860 --> 00:31:51,810 Warsaw LQG: Some tricky results, some tricky. 272 00:31:53,940 --> 00:31:55,920 Warsaw LQG: parts of ourselves, is that 273 00:31:57,240 --> 00:32:01,980 Warsaw LQG: This condition explicitly depends on the on the radius of the horizon. 274 00:32:03,210 --> 00:32:03,930 Warsaw LQG: So, 275 00:32:05,820 --> 00:32:09,180 Warsaw LQG: In general, if we if we have one 276 00:32:11,610 --> 00:32:12,990 Warsaw LQG: Singular horizon. 277 00:32:14,520 --> 00:32:23,010 Warsaw LQG: Then we could ask, what about the up to free other horizons. And in fact, this, this, this condition tells us 278 00:32:24,030 --> 00:32:32,280 Warsaw LQG: That if you make one of the crisis one singular, then there's no no possibility of making other horizons non singular 279 00:32:40,590 --> 00:32:50,880 Warsaw LQG: Yes, so the next. The next thing we consider was where the the neighborhood of the horizons and 280 00:32:52,140 --> 00:33:00,900 Warsaw LQG: To do that we introduced the space of the orbits the orbits of the Kinect oxide and directly the horizon. 281 00:33:03,990 --> 00:33:05,730 Warsaw LQG: And to do that we chose 282 00:33:06,810 --> 00:33:13,290 Warsaw LQG: Chose the coordinates, such as exciting equals to some detail. And in fact, the 283 00:33:16,320 --> 00:33:21,270 Warsaw LQG: If the code is that I'll show you in a minute quite similar to those for the horizon. 284 00:33:22,680 --> 00:33:27,360 Warsaw LQG: And then if we if you can write the metric in this 285 00:33:28,470 --> 00:33:31,440 Warsaw LQG: New Horizons in this form. 286 00:33:32,880 --> 00:33:33,300 Warsaw LQG: Then 287 00:33:36,600 --> 00:34:01,980 Warsaw LQG: Then there are a couple of nice nice things about about this way of writing the metric. So for example, this Q part so que que ha the X the X the X j correspond to the metric on the space of the orbits of the better side. So one could maybe better understand what this metric is 288 00:34:03,060 --> 00:34:07,650 Warsaw LQG: Is if we consider that the the space time 289 00:34:08,670 --> 00:34:09,090 Warsaw LQG: Is 290 00:34:10,110 --> 00:34:14,100 Warsaw LQG: Created by the by the flows on the kinetic side and 291 00:34:17,160 --> 00:34:17,730 Warsaw LQG: Each 292 00:34:20,250 --> 00:34:21,600 Warsaw LQG: And this low corresponds to 293 00:34:23,790 --> 00:34:25,950 Warsaw LQG: The clinic observers and then 294 00:34:26,970 --> 00:34:33,780 Warsaw LQG: Then the skill measure space time distance between between some neighboring kingdoms observers. 295 00:34:35,490 --> 00:34:36,660 Warsaw LQG: Along alongside 296 00:34:39,330 --> 00:34:41,700 Warsaw LQG: So some other some other part is 297 00:34:42,840 --> 00:34:46,170 Warsaw LQG: This one from ditto plus and the dog is 298 00:34:47,250 --> 00:34:48,630 Warsaw LQG: Divided by Jane Doe. 299 00:34:49,980 --> 00:34:50,370 Warsaw LQG: The x 300 00:34:51,750 --> 00:34:52,410 Warsaw LQG: Which is 301 00:34:54,420 --> 00:34:56,940 Warsaw LQG: Which we call the rotation connection one form. 302 00:34:58,140 --> 00:35:06,660 Warsaw LQG: Because it is somehow connected to the to the rotation of the space and also this one firms actually a connection on the 303 00:35:08,130 --> 00:35:11,970 Warsaw LQG: Connection form on the hub bundle which 304 00:35:14,160 --> 00:35:16,380 Warsaw LQG: Of which the our horizon structure. 305 00:35:17,790 --> 00:35:18,750 Warsaw LQG: So, 306 00:35:20,310 --> 00:35:24,600 Warsaw LQG: What's the benefit of writing that the metric in this way. So all of these 307 00:35:25,920 --> 00:35:31,950 Warsaw LQG: All of these objects that they described as well that loves function they have they have 308 00:35:33,600 --> 00:35:45,300 Warsaw LQG: Geometric geometric meaning besides some some coordinated expression. So it's, it's actually good because our considerations about the horizon. We're also 309 00:35:46,650 --> 00:35:56,250 Warsaw LQG: Kind of geometry, because the horizon is a it's an object which is defined geometry geometry and not not in some particular coordinates. 310 00:35:58,170 --> 00:36:01,230 Warsaw LQG: And so this is this is the analytical approach. 311 00:36:02,280 --> 00:36:04,530 Warsaw LQG: In the neighborhood of that the crisis. 312 00:36:07,800 --> 00:36:12,120 Warsaw LQG: Some will we make some particular choice of the of the coordinates. 313 00:36:15,240 --> 00:36:18,240 Warsaw LQG: And this choice is quite similar to the 314 00:36:19,830 --> 00:36:25,380 Warsaw LQG: To the choice for the horizon. So, and before we had Tao equal to some 315 00:36:27,330 --> 00:36:37,200 Warsaw LQG: Advanced code and advice advanced and coordinate. Now we have simply simply team and also there is x one, which is just the radius. 316 00:36:38,550 --> 00:36:43,020 Warsaw LQG: And the rest is is the same as in the horizon case. 317 00:36:46,800 --> 00:36:52,920 Warsaw LQG: And then we can ride the, the original American in this new form. 318 00:36:55,650 --> 00:36:56,370 Warsaw LQG: For me, which we 319 00:36:57,450 --> 00:36:58,020 Warsaw LQG: Extract 320 00:36:59,190 --> 00:37:03,300 Warsaw LQG: The form of the metric on the space of the orbits. 321 00:37:10,440 --> 00:37:23,400 Warsaw LQG: So if you want this this metric to measure distance. Distance between the kink observers, we have to make sure that that we are somehow using the frame which is tangent to the 322 00:37:25,140 --> 00:37:33,180 Warsaw LQG: To the, to the side. So we are introducing introducing new frame this hearted frame. 323 00:37:35,760 --> 00:37:38,490 Warsaw LQG: That exactly satisfies satisfies our property. 324 00:37:39,840 --> 00:37:42,480 Warsaw LQG: Property that is it's it's perpendicular to 325 00:37:45,000 --> 00:37:46,560 Warsaw LQG: The side and 326 00:37:49,650 --> 00:37:52,650 Warsaw LQG: When I say live and this this metric. Q. 327 00:37:54,960 --> 00:37:57,570 Warsaw LQG: On the space of the of the orbits. 328 00:38:01,860 --> 00:38:10,950 Warsaw LQG: And obviously, it has some properties that I would like to discuss now. So first of first of which is the 329 00:38:12,000 --> 00:38:13,500 Warsaw LQG: The signature. 330 00:38:15,720 --> 00:38:19,200 Warsaw LQG: So these components Q human lung. 331 00:38:20,340 --> 00:38:30,630 Warsaw LQG: Close to the horizon, just the non extra mile for aizen which might be some which actually makes a difference here. What kind of Horizon, we do consider 332 00:38:31,470 --> 00:38:47,040 Warsaw LQG: Which wasn't the case, the horizon case on the the previous metric was in qualifying for the for the external horizons or so when when the R zero was a multiple of the function Q 333 00:38:49,230 --> 00:38:52,290 Warsaw LQG: Now we only consider the unknown extreme cases. 334 00:38:54,360 --> 00:39:05,640 Warsaw LQG: So close to the horizon, the cumin. One is proportional to minus g psych side. So when the time is is time like 335 00:39:07,500 --> 00:39:13,380 Warsaw LQG: This component is positive and the other way around. When is space like 336 00:39:14,610 --> 00:39:19,950 Warsaw LQG: To to to buy the assumption that the P is positive. You see, it's also positive everywhere. 337 00:39:21,960 --> 00:39:23,190 Warsaw LQG: And the component 338 00:39:24,270 --> 00:39:24,870 Warsaw LQG: To 339 00:39:26,970 --> 00:39:31,170 Warsaw LQG: The component, feel free. Three also requires us that we are 340 00:39:32,610 --> 00:39:36,900 Warsaw LQG: Supposedly, but only one we are close to the non extra mile horizon. 341 00:39:38,850 --> 00:39:42,420 Warsaw LQG: So this can probably be better seen from from this 342 00:39:44,610 --> 00:39:45,240 Warsaw LQG: Explicit 343 00:39:48,090 --> 00:39:48,930 Warsaw LQG: Form well 344 00:39:51,990 --> 00:40:00,630 Warsaw LQG: Then what we what we did here was just divide by my dysfunction kill and if 345 00:40:01,890 --> 00:40:04,620 Warsaw LQG: In the denominator, the negative part 346 00:40:06,270 --> 00:40:18,330 Warsaw LQG: If it vanishes. Then, then this be science squared 00 squared sigma divided by sigma squared, it's positive. So then we would have 347 00:40:19,740 --> 00:40:20,520 Warsaw LQG: We would have 348 00:40:21,660 --> 00:40:23,250 Warsaw LQG: You feel free positive 349 00:40:24,570 --> 00:40:27,210 Warsaw LQG: And when we consider this this denominator 350 00:40:30,570 --> 00:40:34,560 Warsaw LQG: It goes to zero when we approach the horizon, only if the 351 00:40:35,640 --> 00:40:36,120 Warsaw LQG: If the 352 00:40:37,200 --> 00:40:37,920 Warsaw LQG: R zero 353 00:40:38,940 --> 00:40:41,490 Warsaw LQG: Corresponds to the non singular person. 354 00:40:42,960 --> 00:40:51,060 Warsaw LQG: Otherwise this this second second part. And denominator approaches some concept on even can 355 00:40:52,560 --> 00:40:53,250 Warsaw LQG: Even can 356 00:40:54,450 --> 00:40:56,520 Warsaw LQG: Blow up and this is this is a result 357 00:40:57,630 --> 00:41:01,560 Warsaw LQG: This stems from the fact that the 358 00:41:02,940 --> 00:41:05,640 Warsaw LQG: The metric and and the the space of the 359 00:41:07,620 --> 00:41:13,020 Warsaw LQG: Of the purpose of the killing horizon as well as you find on the way. 360 00:41:15,360 --> 00:41:16,920 Warsaw LQG: If you are far from the horizon. 361 00:41:22,980 --> 00:41:37,770 Warsaw LQG: And this is also some some it's mirrored in the fact that the denominator of the component queue for free. It's actually proportional proportional to the to the length of the 362 00:41:40,560 --> 00:41:41,730 Warsaw LQG: Of the vector side. 363 00:41:42,900 --> 00:41:43,650 Warsaw LQG: So, 364 00:41:45,600 --> 00:41:50,790 Warsaw LQG: If we are close to the to the extra mile for eyes on this component 365 00:41:51,810 --> 00:41:54,120 Warsaw LQG: Feel free. Free to approach the 366 00:41:55,230 --> 00:42:01,200 Warsaw LQG: The component cube for free from the metric on the on the horizon and 367 00:42:03,690 --> 00:42:10,770 Warsaw LQG: That would be fine for us. We have just some extension of the geometry from the horizon to the neighborhood, but 368 00:42:13,410 --> 00:42:18,210 Warsaw LQG: There, there might be some services which are not killing horizons. 369 00:42:21,330 --> 00:42:21,780 Warsaw LQG: And 370 00:42:23,520 --> 00:42:32,670 Warsaw LQG: All the way to the the norm on tech side also vanishes. So that's kind of a natural range of the applicability of our of our metals. 371 00:42:40,350 --> 00:42:48,060 Warsaw LQG: Yes, so. So, the important part here is that that this metric tends to the present metric. If the R zero is a single 372 00:42:49,260 --> 00:42:53,040 Warsaw LQG: Singular it corresponding to the non western horizon. 373 00:42:56,760 --> 00:43:00,690 Warsaw LQG: So the considerations from the previous slide, it has to the conclusion that 374 00:43:01,980 --> 00:43:07,560 Warsaw LQG: First, we, we should consider here on the, the non external four zones. 375 00:43:08,700 --> 00:43:22,260 Warsaw LQG: So are in order to to assure that our signature is either plus, plus, plus or minus plus plus one. What's really important for us is that, and that 376 00:43:23,700 --> 00:43:25,380 Warsaw LQG: There are two classes at the end here. 377 00:43:27,330 --> 00:43:28,080 Warsaw LQG: And also, 378 00:43:29,370 --> 00:43:34,950 Warsaw LQG: There are a couple of statements that dependent on the fact that we are close to the horizon. So in fact, 379 00:43:35,970 --> 00:43:36,690 Warsaw LQG: Our metric 380 00:43:38,130 --> 00:43:44,670 Warsaw LQG: Or a metric is defined on the on some on some future or past neighborhood on the horizon. 381 00:43:47,250 --> 00:43:47,790 Warsaw LQG: And this 382 00:43:49,470 --> 00:43:50,580 Warsaw LQG: Is a short assures us that 383 00:43:51,990 --> 00:43:54,120 Warsaw LQG: That excite does not doesn't vanish. 384 00:43:55,470 --> 00:43:55,950 Warsaw LQG: And 385 00:43:57,360 --> 00:44:00,660 Warsaw LQG: And this component to free free is well defined. 386 00:44:06,060 --> 00:44:06,660 Warsaw LQG: So, 387 00:44:08,250 --> 00:44:09,480 Warsaw LQG: Again, we want to 388 00:44:11,310 --> 00:44:12,600 Warsaw LQG: We want to consider. 389 00:44:17,250 --> 00:44:28,770 Warsaw LQG: Want to consider whether this metric is is analytic and of course it should be analytic everywhere was defined, apart from the posts on the same case as the horizon. 390 00:44:30,240 --> 00:44:32,310 Warsaw LQG: And then the only the only 391 00:44:35,670 --> 00:44:44,340 Warsaw LQG: The only part of this metric, which can be which can be singled out the post have some problems is the pullback of this metric to to the surfaces. 392 00:44:45,570 --> 00:44:56,580 Warsaw LQG: With the surfaces of X one constant but not equal to the horizon radios will, which was the case that when considered earlier. 393 00:45:01,980 --> 00:45:04,500 Warsaw LQG: For this for this two dimensional matrix. 394 00:45:06,120 --> 00:45:10,890 Warsaw LQG: We can look in again use the framework of considering loops. 395 00:45:11,940 --> 00:45:12,780 Warsaw LQG: loops around 396 00:45:14,610 --> 00:45:15,870 Warsaw LQG: The rotational axis. 397 00:45:17,880 --> 00:45:26,580 Warsaw LQG: So the, the circumference of the circle and the radius are defined just just in the same way as for the horizon. 398 00:45:31,440 --> 00:45:42,030 Warsaw LQG: And what we somewhat surprisingly discovered is that when we apply this framework of of loops and we impose this condition that 399 00:45:42,540 --> 00:45:58,050 Warsaw LQG: And that the ratio of circumference to the radius should be two pi in the post that we recover exactly the same condition is for the horizon, so that P zero equals to some friction and then p of by 400 00:45:59,580 --> 00:46:00,120 Warsaw LQG: And 401 00:46:01,980 --> 00:46:06,600 Warsaw LQG: So what it means is that if we can some some 402 00:46:07,770 --> 00:46:16,110 Warsaw LQG: Parameters that I've made no single our horizon, then at the same time simultaneously those parameters. 403 00:46:16,920 --> 00:46:30,420 Warsaw LQG: Remove the singularity from the, from the future or past neighborhood of the horizon. And what's also important to stress here is that the our rescaling constant is still simply one over 404 00:46:31,710 --> 00:46:40,980 Warsaw LQG: You know, and the function PR zero does not depend on the value on the coordinate or here on the x coordinate, so 405 00:46:44,880 --> 00:46:45,930 Warsaw LQG: So, 406 00:46:48,450 --> 00:46:58,260 Warsaw LQG: So on the all of the surface. That's funny. The, the neighborhood of the horizon. We use exactly the same rescaling as the as the horizon, so we can make 407 00:47:00,360 --> 00:47:08,040 Warsaw LQG: The horizon and the the past or future neighborhood one singular simultaneously with their horizon. 408 00:47:15,060 --> 00:47:16,260 Warsaw LQG: Yes. So, so 409 00:47:18,600 --> 00:47:23,040 Warsaw LQG: So that was our main results that we will cover this 410 00:47:25,230 --> 00:47:28,590 Warsaw LQG: Condition for the non singularity and then salted 411 00:47:29,790 --> 00:47:40,980 Warsaw LQG: So it's so you can see the first, the general case of the kernel space time privatized by massacre perimeter not parameter and lambda 412 00:47:44,130 --> 00:47:50,100 Warsaw LQG: We examine the geometry of the non generic horizon. And what we found is that 413 00:47:52,560 --> 00:48:01,980 Warsaw LQG: Consistent with the previous previous statements in the literature, generally, but the general generic values of the parameters the singularity is 414 00:48:04,140 --> 00:48:08,130 Warsaw LQG: Non removable in at least one of the and the polls. 415 00:48:10,620 --> 00:48:16,950 Warsaw LQG: Then we will post this condition down to the radius that the ratio of the circumference 416 00:48:18,000 --> 00:48:23,550 Warsaw LQG: And the ratio of the loops around the rotational axis as to tend to two pi. 417 00:48:25,380 --> 00:48:43,440 Warsaw LQG: In the polls. These gave us the condition for removing the singularity, which we solve and obtain the new and new solution. So this constraint lambda equals two free over a squared plus two squared plus two, or zero squared. 418 00:48:44,880 --> 00:48:50,640 Warsaw LQG: So that was our new result and also our conditional recovered the previous know 419 00:48:52,200 --> 00:48:53,730 Warsaw LQG: The previously known singer. 420 00:48:56,160 --> 00:48:57,240 Warsaw LQG: Solutions. So 421 00:48:58,350 --> 00:49:04,500 Warsaw LQG: Curve the theater space times and not the center around like to sit there your space times 422 00:49:05,850 --> 00:49:06,300 Warsaw LQG: And 423 00:49:10,260 --> 00:49:13,710 Warsaw LQG: Just think, fear is that there is still this 424 00:49:15,990 --> 00:49:19,410 Warsaw LQG: somewhat surprising for us part that 425 00:49:22,140 --> 00:49:31,530 Warsaw LQG: We can also we can make at least at most one of the horizon, no singular at the time because our constraints explicitly 426 00:49:32,850 --> 00:49:36,060 Warsaw LQG: Depends on the value or the radius of their horizon. 427 00:49:39,630 --> 00:49:43,770 Warsaw LQG: So next we we consider also 428 00:49:45,150 --> 00:49:50,400 Warsaw LQG: The neighborhood of the non singular prisons. So employed the framework of the 429 00:49:51,720 --> 00:49:52,860 Warsaw LQG: Space of the 430 00:49:53,940 --> 00:49:55,170 Warsaw LQG: orbits of the healing. 431 00:49:56,430 --> 00:49:58,740 Warsaw LQG: Vector developing the horizon. 432 00:49:59,850 --> 00:50:03,870 Warsaw LQG: And we found that it has a good properties in the known external case. 433 00:50:06,450 --> 00:50:12,810 Warsaw LQG: But we have to restrict ourselves to some small neighborhood of the horizon. 434 00:50:14,160 --> 00:50:15,660 Warsaw LQG: It should be zero here. 435 00:50:17,670 --> 00:50:20,520 Warsaw LQG: And then our metric metric 436 00:50:22,140 --> 00:50:27,960 Warsaw LQG: On the model space is well defined and has the signature. Not that we want actually 437 00:50:29,370 --> 00:50:36,060 Warsaw LQG: So our neighbors was his the topology of a sweet time some some interval around 438 00:50:37,620 --> 00:50:45,120 Warsaw LQG: Around the horizon. And in fact, each of the horizon has the topology of the abandoned. 439 00:50:46,260 --> 00:50:47,790 Warsaw LQG: Over, over a stone. 440 00:50:50,490 --> 00:50:51,120 Warsaw LQG: So, 441 00:50:53,910 --> 00:50:59,910 Warsaw LQG: I will research as I, as I said in the beginning, originated from from the quest to find 442 00:51:01,560 --> 00:51:02,400 Warsaw LQG: To to embed 443 00:51:03,420 --> 00:51:11,610 Warsaw LQG: All of the type deep, but from the path of typing and vacuum isolated horizons, which were 444 00:51:15,120 --> 00:51:15,630 Warsaw LQG: Which were 445 00:51:18,120 --> 00:51:22,950 Warsaw LQG: Found in some more abstract way we wanted to 446 00:51:23,970 --> 00:51:30,750 Warsaw LQG: To know how they correspond to into the unknown metrics. How are they embeddable 447 00:51:31,920 --> 00:51:36,300 Warsaw LQG: And Don'ts horizons on and non trivial to political bundle. 448 00:51:38,160 --> 00:51:40,410 Warsaw LQG: There were four dimensional family. 449 00:51:41,610 --> 00:51:42,660 Warsaw LQG: And because 450 00:51:44,100 --> 00:51:44,670 Warsaw LQG: Our 451 00:51:46,590 --> 00:52:02,880 Warsaw LQG: Our horizons are not singular only if we pull someone constraint on the cosmetic constant. We only have a three dimensional sub family. So the next quite obvious question is, was about the remaining time horizons and 452 00:52:06,360 --> 00:52:12,600 Warsaw LQG: We what we consider next where the accelerated cannot enter the Sitter space time 453 00:52:14,100 --> 00:52:28,020 Warsaw LQG: So one course, one can interpret the space time as a min similarity to the case of the current not under this space time but the black hole is also some some acceleration 454 00:52:30,000 --> 00:52:35,520 Warsaw LQG: Along the singular access and does it gives us a new degree of freedom. 455 00:52:38,070 --> 00:52:40,260 Warsaw LQG: Which we conjecture that can be 456 00:52:41,610 --> 00:52:51,750 Warsaw LQG: Connected to the fourth fourth dimensional and fourth dimension on this family have better update Dean biking horizon some some mantra that bundle. 457 00:52:54,720 --> 00:53:01,440 Warsaw LQG: And in fact, when we consider this case we arrived at exactly the same condition. 458 00:53:02,730 --> 00:53:05,190 Warsaw LQG: For the removing removing of 459 00:53:07,200 --> 00:53:08,220 Warsaw LQG: Of the singularity. 460 00:53:11,430 --> 00:53:16,710 Warsaw LQG: We employed the same framework we arrived at the end result that was formerly the same 461 00:53:18,060 --> 00:53:26,880 Warsaw LQG: So remember this condition constrained with with p zero P of by. So, this condition is the same. 462 00:53:27,960 --> 00:53:28,740 Warsaw LQG: But 463 00:53:30,000 --> 00:53:35,790 Warsaw LQG: The form of this P function diverse it's somewhat more complicated for the accelerated case. 464 00:53:37,110 --> 00:53:39,360 Warsaw LQG: And we also solve this 465 00:53:43,170 --> 00:53:55,500 Warsaw LQG: So this constraint and right there's some four dimensional family of accelerated current not on data center space time that meetings non singular horizons and neighborhoods and 466 00:53:57,210 --> 00:54:04,950 Warsaw LQG: Here there's an additional benefit that the constraint that we should have a positive because Minister constant, this 467 00:54:07,440 --> 00:54:12,060 Warsaw LQG: Is relaxed. So we don't mean some some negative customer for constant also 468 00:54:13,590 --> 00:54:14,070 Warsaw LQG: So, 469 00:54:15,630 --> 00:54:19,800 Warsaw LQG: More details about our methods about our resolve. 470 00:54:21,150 --> 00:54:27,240 Warsaw LQG: should appear in the upcoming paper some some time, we have this mouth and 471 00:54:28,560 --> 00:54:31,740 Warsaw LQG: It was not the answer questions. Thanks. Thank you for your attention. 472 00:54:55,980 --> 00:54:56,700 Penn State: No. Can you hear me. 473 00:54:58,200 --> 00:54:59,010 Warsaw LQG: I can hear you now. 474 00:54:59,940 --> 00:55:04,110 Penn State: Okay, so this is like a couple questions. The first is 475 00:55:05,280 --> 00:55:07,170 Penn State: If you go back to slide 14 476 00:55:09,870 --> 00:55:15,780 Penn State: Yeah, so you're looking for known singular certain non non solutions are, I guess. 477 00:55:16,800 --> 00:55:21,630 Penn State: It's like 30 you're looking at non singular solutions solutions with non single horizons. Right. 478 00:55:22,110 --> 00:55:30,240 Penn State: 13 or 1413 you're looking at general conditions you wrote down the slide. You're all done. And then in the next slide. 479 00:55:30,270 --> 00:55:30,930 Warsaw LQG: 14 480 00:55:31,230 --> 00:55:33,570 Penn State: Years give non non singular solutions. 481 00:55:34,860 --> 00:55:36,780 Penn State: Why so what happens to 482 00:55:39,480 --> 00:55:42,000 Penn State: The Singularity persistent. What's the story. 483 00:55:42,330 --> 00:55:46,500 Warsaw LQG: Yes incarnate. You cannot remove the singularity. Okay. 484 00:55:47,400 --> 00:55:47,760 Thank you. 485 00:55:49,530 --> 00:55:57,390 Penn State: The product question is the following that. I don't know if I understood the main message but i mean you know your result is that 486 00:55:58,590 --> 00:55:59,640 Penn State: Let's consider this 487 00:56:00,750 --> 00:56:10,170 Penn State: This for parameter family of solutions. And of course, it is of interest to consider the case where the generic case where none of the parameters is zero right 488 00:56:11,010 --> 00:56:11,340 Warsaw LQG: Yes. 489 00:56:11,610 --> 00:56:13,230 Penn State: And then in that case, sort of, 490 00:56:14,400 --> 00:56:18,870 Penn State: Your results implied that whether the cosmology of constant is positive or negative. 491 00:56:19,890 --> 00:56:21,780 Penn State: There is no way to get rid of. 492 00:56:22,800 --> 00:56:25,290 Penn State: The conical singularity on all the prizes. 493 00:56:28,320 --> 00:56:31,590 Warsaw LQG: Yes. So our clustering depends on the radio surprising sober, I 494 00:56:33,720 --> 00:56:34,320 Penn State: Might be able to 495 00:56:34,350 --> 00:56:40,770 Penn State: Choose your parameters and I mean if you like can be thought of as r&r or not depends on everything else. 496 00:56:42,270 --> 00:56:45,240 Penn State: So you can choose your parameters MN lambda 497 00:56:47,550 --> 00:56:47,850 And 498 00:56:49,860 --> 00:56:53,910 Penn State: L an A. Yeah, so you can choose those parameters, such that 499 00:56:56,730 --> 00:57:03,210 Penn State: Such that one or eyes and everything is fine, but then something will be wrong adopt another reason normally one sort of 500 00:57:04,380 --> 00:57:11,970 Penn State: Physically one is interested in solutions which don't have Monica singularities. Anyway, that was the main point of it. Is there any other people. Right. 501 00:57:12,480 --> 00:57:20,100 Penn State: Because of our clinical singularity is that means that there is a Einstein's equation or some stress any answer which corresponds to membrane no order. 502 00:57:21,630 --> 00:57:22,920 Penn State: So then 503 00:57:23,940 --> 00:57:26,730 Penn State: My take home message I took it to be that 504 00:57:28,500 --> 00:57:34,800 Penn State: The case with all four parameters non zero is physically not interesting. Am I missing something. 505 00:57:40,890 --> 00:57:41,130 Warsaw LQG: In 506 00:57:41,340 --> 00:57:43,980 Penn State: This case, irrespective of the sign of the cosmos actual cost and 507 00:57:45,330 --> 00:57:49,350 Penn State: It will be Hanukkah singularity is somewhere in the space time 508 00:57:50,460 --> 00:57:56,340 Warsaw LQG: It's so surprising results for us. Also, we also don't fully understand 509 00:57:58,320 --> 00:57:59,730 Warsaw LQG: Why this is the case. 510 00:58:01,110 --> 00:58:03,120 Warsaw LQG: Especially the the reason 511 00:58:03,840 --> 00:58:05,550 Penn State: Why this is the case, I'm just saying that if 512 00:58:06,060 --> 00:58:08,250 Penn State: Assuming that this is the case, which is your result. 513 00:58:08,850 --> 00:58:14,700 Penn State: Then I will just conclude that, that, that, that is, it implies that therefore 514 00:58:15,750 --> 00:58:16,170 The 515 00:58:17,850 --> 00:58:21,690 Penn State: Space times with all for panorama does not equal to zero or physically not interesting. 516 00:58:22,890 --> 00:58:30,840 Penn State: Because they will always have some why single I mean this sheet of singularity right this conical singularity between 517 00:58:32,340 --> 00:58:33,210 Penn State: idolizes 518 00:58:36,510 --> 00:58:38,220 Warsaw LQG: Results in place, right. 519 00:58:38,790 --> 00:58:39,390 Penn State: So you can hear. 520 00:58:39,480 --> 00:58:39,660 Penn State: Me. 521 00:58:39,720 --> 00:58:43,920 FAU Erlangen: And I can I can I help much, much, you can also 522 00:58:44,250 --> 00:58:58,230 FAU Erlangen: Yeah please elaborate on your question. Okay, so, so this is the zero to order conclusion that that this singularity cannot be removed all space. I mean, now this 523 00:58:59,250 --> 00:59:08,130 FAU Erlangen: peculiar property. Is that still for some special a choice of the cosmological constant 524 00:59:09,210 --> 00:59:16,500 FAU Erlangen: In neighborhood. One of the horizons becomes non singular and and its neighborhood is also 525 00:59:18,240 --> 00:59:23,370 FAU Erlangen: So, well, maybe it's not enough for you if you would like all the space time to be 526 00:59:23,970 --> 00:59:32,160 Penn State: Yeah, because that's what anybody would say, right, anybody would say that if I want to take the space time. Can you speak to be interesting. It is not enough that one neighborhood is this 527 00:59:32,670 --> 00:59:36,840 FAU Erlangen: So it depends on who we're talking to, if somebody is not interested in 528 00:59:40,260 --> 00:59:41,640 Nothing interesting 529 00:59:43,980 --> 00:59:46,620 Penn State: Exactly. The question I wanted to answer. 530 00:59:47,520 --> 00:59:52,950 FAU Erlangen: It is in between subtlety that are those horizons in 531 00:59:54,180 --> 01:00:04,200 FAU Erlangen: This Theater, which in some special for the values of cosmological constant are in non singular and also they are surrounded by non singular 532 01:00:04,980 --> 01:00:18,330 FAU Erlangen: Neighborhood. But let me also say something more. So in fact, we show that we're results to people who who are who wrote earlier some papers on not 533 01:00:18,900 --> 01:00:31,860 FAU Erlangen: Space times is actually our statement that generically those horizons have this unremovable clinical singularity is not something which is commonly 534 01:00:32,790 --> 01:00:46,440 FAU Erlangen: Believed and understood, people usually think that the singularity follows because of this non trivial topological character. And if we properly. 535 01:00:46,830 --> 01:00:53,130 FAU Erlangen: Glue space time then we grew one singular part was another non singular part and we 536 01:00:54,030 --> 01:01:01,260 FAU Erlangen: Don't have singularity at all. This is I think Mark Mars, send us the reference to some paper in which 537 01:01:01,560 --> 01:01:09,570 FAU Erlangen: This is explicitly stated, however, nobody proves this is just written as some remark that obviously if we create space I'm that we don't have 538 01:01:10,080 --> 01:01:32,700 FAU Erlangen: This clinical singularity. So, so the generic. So this take home message which you want to take it is also something something new because you may find statements in literature that actually there is no clinical singularity. If you properly. A extend this space time by this political glue 539 01:01:35,760 --> 01:01:38,760 Penn State: So is that true that, in this case, then if you 540 01:01:40,350 --> 01:01:43,650 Penn State: Have appropriate political identifications you can remove 541 01:01:45,300 --> 01:01:54,330 Penn State: The clinical singularity everywhere in space time when in the, in the case that is on the, on the, on the slide right night right now, which is that none of the parameters is equal to zero. 542 01:01:55,980 --> 01:01:59,760 FAU Erlangen: Know, I will resolve shows you can have 543 01:02:00,150 --> 01:02:12,660 Penn State: Yeah, so right so sauce. So I'm still don't understand. You said that you talked to some people and they were saying that this is a space types of physical interest and I'm very curious to know 544 01:02:14,730 --> 01:02:16,710 Penn State: What would be the physical application. 545 01:02:22,620 --> 01:02:27,000 FAU Erlangen: Well, this is a good, good question. I, I'm not sure. 546 01:02:28,890 --> 01:02:45,180 Penn State: So I just wanted to say that, you know, many, many years ago, I looked at also the the see metric, which has clinical singularity generically. It has parameters which is mass acceleration. And you can also enter the charge. And if you're all these see 547 01:02:46,260 --> 01:02:57,900 Penn State: Charges nonzero bed. In fact, you can do exactly what we have here on this slide. Maybe you can choose a particular value of charge, which is given by the other parameters, such that there is no clinical singularity. 548 01:02:59,160 --> 01:03:09,300 Penn State: But in that case it is there's no clinical singularity anywhere is based on that because they just to black hole. So it's not so complicated, like a cosmological horizon some black hole arises and so 549 01:03:10,950 --> 01:03:18,720 Penn State: So I think that's that's the reason why I'm very interested in this because it looked to me that it has some features like the charge symmetric 550 01:03:20,310 --> 01:03:30,750 Penn State: Okay. And the question was what along the way, did you learn anything striking or interesting or just as a side remark about the courtesy to our case. 551 01:03:32,040 --> 01:03:33,720 Penn State: You know those eloquent zero case. 552 01:03:37,650 --> 01:03:47,370 Warsaw LQG: So our patients and this is constantly reminds us that they don't work for the lambda zero and so 553 01:03:48,840 --> 01:03:50,070 Warsaw LQG: So I think that no 554 01:03:52,800 --> 01:03:53,610 Okay, thank you. 555 01:03:54,660 --> 01:03:55,020 Warsaw LQG: Thank you. 556 01:03:57,330 --> 01:04:02,220 Gravity Group, Univ. Wroclaw: Hello. So what is something maybe from the side. Let me get a little car from rosov 557 01:04:03,060 --> 01:04:03,330 Out. 558 01:04:04,650 --> 01:04:24,630 Gravity Group, Univ. Wroclaw: Okay, so I would like to learn more about your constraint between cosmological constant, this, this condition with our zero square where it came from. You said that gluing is not enough. So this is some kind of differentiable result, I don't know, like how to this and where you got this 559 01:04:28,980 --> 01:04:30,930 Warsaw LQG: So you're talking about this condition. 560 01:04:30,960 --> 01:04:32,400 Gravity Group, Univ. Wroclaw: Yes, yes. 561 01:04:32,460 --> 01:04:33,060 Warsaw LQG: Yes, exactly. 562 01:04:34,710 --> 01:04:35,490 Warsaw LQG: So, it 563 01:04:36,660 --> 01:04:39,750 Warsaw LQG: Comes from solving this this equation. 564 01:04:40,920 --> 01:04:44,010 Warsaw LQG: This constraint which which to arrive at by 565 01:04:44,790 --> 01:04:45,840 Warsaw LQG: Requiring that 566 01:04:45,960 --> 01:04:48,150 Warsaw LQG: The limit is to buy 567 01:04:49,980 --> 01:04:55,530 Gravity Group, Univ. Wroclaw: So this is just some kind of consistency condition between on two poles. 568 01:04:55,980 --> 01:04:58,890 Gravity Group, Univ. Wroclaw: Yes, somebody with some kind of light colored say 569 01:05:00,030 --> 01:05:05,250 Gravity Group, Univ. Wroclaw: One expression multiplying P pie and another expression multiplying p zero 570 01:05:06,480 --> 01:05:18,600 Gravity Group, Univ. Wroclaw: So it's some kind of consistency condition between the polls, because let me say a couple reminders, because I was playing in the past about hope not. Space name. He also had one slide with my 571 01:05:19,050 --> 01:05:41,070 Gravity Group, Univ. Wroclaw: My work. So basically, I noticed that behavior of this strings to be somehow like representing a rotation like basically you can have another set of killing vectors and just consider that you have a constant angular velocity and then that explains somehow why this taupe 572 01:05:42,210 --> 01:05:51,840 Gravity Group, Univ. Wroclaw: List is not parameter actually is very similar to the care parameter in the formulas. Somehow it like a represents that projection on busy access even 573 01:05:52,110 --> 01:06:04,200 Gravity Group, Univ. Wroclaw: When you look closer to the formulas and basically along the way I wanted to, to, to leave this to canonical a clinical singularities basically 574 01:06:04,710 --> 01:06:11,400 Gravity Group, Univ. Wroclaw: Represent the black hole peers five at cosmic string, which was rotating or to cosmic strings rotating 575 01:06:11,970 --> 01:06:28,590 Gravity Group, Univ. Wroclaw: And then basically, I wanted to leave this space them as it is hoping that I will get some kind of maybe another kind of condition consistency condition which would like avoid glowing about maybe along the way, having something. So you have some kind of condition which looks 576 01:06:29,820 --> 01:06:38,100 Gravity Group, Univ. Wroclaw: In the, in the service philosophy, but you want always to remove this severity. So it's like Mark 577 01:06:38,850 --> 01:06:42,840 Warsaw LQG: Is also, we do want to make this glowing 578 01:06:43,320 --> 01:06:44,700 Warsaw LQG: Hmm, contrary to 579 01:06:46,140 --> 01:06:47,100 Warsaw LQG: What you're trying to do. 580 01:06:48,030 --> 01:07:00,660 Gravity Group, Univ. Wroclaw: I just wanted to do, like, see what what is possible to learn more about this metric, as it is right along the way. I don't have any conclusions, but I notice couple of of really strange kind of papers. 581 01:07:01,740 --> 01:07:08,940 Gravity Group, Univ. Wroclaw: Really like the rotation rotating character of this kind of things, not only the kind of like mass parameters stuff. 582 01:07:12,660 --> 01:07:30,120 FAU Erlangen: I would like to add something to the reply which magic, magic sauce. So the question was what is actually non singular if we still can glue do gluing of two to two sections. So, in 583 01:07:30,930 --> 01:07:44,370 FAU Erlangen: Our space time couple logically has structure on this hub bundle times some to other dimensions which I can tractable, so they don't make topology. They don't change anything, and now 584 01:07:45,450 --> 01:07:55,230 FAU Erlangen: There are some objects on on bundle which are engaged set gauge dependent or section dependent. However, there are some structures which are 585 01:07:55,680 --> 01:08:06,960 FAU Erlangen: Independent and would we consider is the space of fibers and the space of fibers is geometric object that this is a choice of slice independent 586 01:08:07,620 --> 01:08:21,840 FAU Erlangen: And if this space of fibers has a problem has some differential ability then choosing sections is not helping so so space of fibers is this invariant object. 587 01:08:22,710 --> 01:08:36,270 FAU Erlangen: Is defined in independently on on choice of coordinates. So we consider. So the bottom line is we consider some property, which is independent of choice of coordinates. 588 01:08:42,390 --> 01:08:43,410 Jorge Pullin: Any other questions. 589 01:08:46,380 --> 01:08:47,880 FAU Erlangen: Actually I have I have still 590 01:08:48,960 --> 01:08:55,200 FAU Erlangen: Answer, maybe, maybe some extension of my answer, which I gave to buy. So I buys 591 01:08:57,360 --> 01:09:07,530 FAU Erlangen: A conclusion from this, from this result was that it because, as we say space time can be made non singular only in the 592 01:09:08,250 --> 01:09:20,580 FAU Erlangen: At most, for one horizon and only neighborhood of this horizon. So it is not physically. It cannot be physically interesting I think this is not something which we check that. 593 01:09:21,030 --> 01:09:34,110 FAU Erlangen: Actually, it can happen for the outer most horizon. So if we if this outermost horizon is non singular, then it's possible that maybe we can extend this 594 01:09:34,950 --> 01:09:43,470 FAU Erlangen: We can remove singularity, all the way from from this horizon to to to all the for all the values of 595 01:09:44,010 --> 01:09:58,710 FAU Erlangen: Of our, of course, still those cabinet space times have they another simplistically flights. So, so I can say, we can do it all the way to describe, but we can do it all the way to infinity of our perhaps this is a construction. 596 01:10:00,270 --> 01:10:08,010 Penn State: Thank you. First of all, thank you very much for your clarification, with the previous clarification, which is that that what you're doing is on the on the space of 597 01:10:09,360 --> 01:10:13,890 Penn State: Generators. And so that really is very important time in that. And that's why 598 01:10:15,930 --> 01:10:29,340 Penn State: Not because if the space generators singularity is much more serious than some cross section is it so thank you for your last answer. The point is that such a space, time, and even 599 01:10:31,020 --> 01:10:31,440 Penn State: The sitter. 600 01:10:34,440 --> 01:10:48,330 Penn State: Would have many several prizes. So just looking so what will happen is that just to get out to most wonders interesting that, then the exterior of the outermost is perfectly fine, but then there will be 601 01:10:49,410 --> 01:11:04,680 Penn State: Kind of kind of comical singularity is in between the two other horizons. Right. I mean, you can you go through your reasons. And so the statement is that they'll be conical singularity in the two other lines, but maybe what you would like to say something like 602 01:11:05,940 --> 01:11:09,060 Penn State: For some reason, physical reason you might be able to argue that 603 01:11:10,350 --> 01:11:11,040 Penn State: Only the 604 01:11:12,060 --> 01:11:24,330 Penn State: The part outside the outermost horizon is what is of interest, but you have to check if that horizon as a cosmological horizon, or is it a black hole of horizon, or what kind of horizon, it is or is a new kind of. So thank you very much. 605 01:11:24,570 --> 01:11:33,570 FAU Erlangen: Yes, yes, that's true, that this is outermost horizon may well be a cosmological horizon and this is also something we don't know for sure. 606 01:11:37,800 --> 01:11:38,670 Jorge Pullin: Any more questions. 607 01:11:39,150 --> 01:11:43,530 Gravity Group, Univ. Wroclaw: Whether you want to have you look at hyperbolic version of because 608 01:11:44,400 --> 01:11:56,640 Gravity Group, Univ. Wroclaw: The paper by Robert month where they consider playing with hyperbolic coconut and some kind of special limits were not parameter has like a cosmological constant 609 01:11:57,630 --> 01:12:16,530 Gravity Group, Univ. Wroclaw: Expression and then there is some kind of duality with like a care. So this hyper bowling one have minuses in some places and that allowing you to kind of certain limits that something is going away. But basically, there is a relation between not parameter and cosmological constant 610 01:12:18,210 --> 01:12:20,430 Gravity Group, Univ. Wroclaw: So that's it. Have you, have you look at it, summer. 611 01:12:21,480 --> 01:12:28,650 Gravity Group, Univ. Wroclaw: Consider if it doesn't change something, if you have another relation between an a parameter and cosmological constant 612 01:12:30,750 --> 01:12:35,130 Warsaw LQG: Well, we haven't looked at this work actually so so 613 01:12:36,360 --> 01:12:37,950 Warsaw LQG: On the fire on the answer. 614 01:12:38,520 --> 01:12:39,330 Warsaw LQG: Would change. 615 01:12:40,950 --> 01:12:44,400 Warsaw LQG: If you can send us that will look at it. Okay. 616 01:12:44,670 --> 01:12:45,420 Warsaw LQG: This paper. 617 01:12:46,560 --> 01:12:59,280 FAU Erlangen: And didn't work in that work is the shape of slice of the horizon is all the while this horizon is a bundle over to or 618 01:12:59,310 --> 01:13:00,870 Gravity Group, Univ. Wroclaw: Over some some 619 01:13:01,620 --> 01:13:13,980 Gravity Group, Univ. Wroclaw: I just like, I don't really need it, but it was not care, too. I like Ultra spinning terror on this another side of duality. So I don't know exactly what is whether you send the paper and hopefully 620 01:13:16,800 --> 01:13:17,100 FAU Erlangen: Thanks. 621 01:13:21,360 --> 01:13:21,990 Jorge Pullin: Anything else 622 01:13:26,520 --> 01:13:27,870 Jorge Pullin: Okay, let's thank the speaker again.