0 00:00:02,370 --> 00:00:06,330 Jorge Pullin: Our speaker today is much is called an upscale who will speak about gravitational 1 00:00:06,330 --> 00:00:07,799 Jorge Pullin: Waves in the sitter universe. 2 00:00:09,630 --> 00:00:12,900 Maciej Kolanowski: And thank you for the introduction and for the opportunity to 3 00:00:13,920 --> 00:00:18,930 Maciej Kolanowski: Speak here. So I would I want to tell you something about 4 00:00:20,190 --> 00:00:38,310 Maciej Kolanowski: Some very recent progress in description of gravitational waves in the presence of positive cosmological constant. Well, I know that it is not a look. Quantum Gravity topic, but I hope that you're still going to be interested in this. 5 00:00:40,920 --> 00:00:58,710 Maciej Kolanowski: And so I will start with some motivation. Why actually in 2020 usual, we should care about gravitational waves and the I will try to convince you that there's still a lot of stuff we don't know. We don't understand 6 00:01:00,330 --> 00:01:11,130 Maciej Kolanowski: And then I will present our free mainly results from this paper that was mentioned on the previous slide. So first of all, 7 00:01:12,390 --> 00:01:19,170 Maciej Kolanowski: Muslims for Emily and it's cry. And so we derived 8 00:01:20,430 --> 00:01:32,340 Maciej Kolanowski: Formula for the changes of energy in financial period in final interviews intervals of time what what amount of energy was emitted. 9 00:01:32,850 --> 00:01:49,260 Maciej Kolanowski: In contrast with previous work when only the total energy emitted was calculated and then then we'll also show you similar energy flux for the horizon and 10 00:01:50,520 --> 00:01:56,910 Maciej Kolanowski: For a thing that for the first time, and we're going to see that. 11 00:01:57,900 --> 00:02:08,580 Maciej Kolanowski: You can take limit with lambda going to zero at the customer at a cosmological horizon, actually, because we have a lot of those in this universe. 12 00:02:08,970 --> 00:02:23,910 Maciej Kolanowski: And you can go with them that zero and actually see horizon and becoming cry, not only on the picture on the background about actually from the point of view of the dynamic of fields. 13 00:02:25,590 --> 00:02:26,400 Maciej Kolanowski: And 14 00:02:27,480 --> 00:02:42,510 Maciej Kolanowski: Last but not least, will also discuss some issues concerned with the fact that time and spatial translations in the Citigroup, and do not commute and what does it mean 15 00:02:43,770 --> 00:02:50,040 Maciej Kolanowski: For the definition of energy and whether does it make sense or not. 16 00:02:51,450 --> 00:03:12,300 Maciej Kolanowski: Okay. Actually, I was told that I talk too fast. So if I talk too fast, don't hesitate to tell me this, or as question or whatever you want. So moving on the what, why should we care about the gravitational waves. Well, first of all, because we actually know that there's some real fundamental 17 00:03:13,770 --> 00:03:21,570 Maciej Kolanowski: And it's kinda surprisingly new and that we really know that they're real. 18 00:03:21,840 --> 00:03:35,670 Maciej Kolanowski: So it's definitely worth pushing better understanding of gravitational waves because, well, it's physics, it's not so this topic is somehow connected to experiment. 19 00:03:36,960 --> 00:03:41,250 Maciej Kolanowski: And not only to some abstract mathematical structures. 20 00:03:42,570 --> 00:03:43,530 Qiaoyin Pan: And so 21 00:03:43,590 --> 00:03:56,700 Maciej Kolanowski: This will. This is the first part of our title gravitational waves. But we also have the sitter universe and obviously what Oh, when I say this, either. I mean, that lambda is 22 00:03:59,430 --> 00:04:08,610 Maciej Kolanowski: Typically positive. So, and no no anti testator things no holography whatsoever here. 23 00:04:10,140 --> 00:04:15,390 Maciej Kolanowski: And we know that, again, this is physical and because 24 00:04:16,620 --> 00:04:35,760 Maciej Kolanowski: Our observation shows us that acceleration is the dead expansion of the universe is accelerating. So we have positive logical construct of us, we will have some public pension here and it's not so clear, but I think the, just the fact 25 00:04:36,720 --> 00:04:55,560 Maciej Kolanowski: That it is positive is nobody doubt that was it. We don't understand nature of cosmological constant, whether it is some fundamental Konstanz of nature or it is simply potential energy of some background field. We didn't know it it 26 00:04:56,400 --> 00:05:03,570 Maciej Kolanowski: For simplicity we assume the to our background is simply disappear universe. So we have 27 00:05:04,800 --> 00:05:08,370 Maciej Kolanowski: So this constant is really a physical constant 28 00:05:10,410 --> 00:05:11,370 Maciej Kolanowski: Okay movie gun. 29 00:05:17,460 --> 00:05:18,210 Maciej Kolanowski: Is 30 00:05:26,010 --> 00:05:26,250 OK. 31 00:05:27,510 --> 00:05:36,330 Maciej Kolanowski: OK, so the problem because actually both those topics are present from the very beginning of 32 00:05:38,640 --> 00:05:43,380 Maciej Kolanowski: Our present from the very beginning of general relativity. So, in 33 00:05:44,610 --> 00:05:58,740 Maciej Kolanowski: Moral more than 100 years ago. Einstein was concerned with positive with cosmological radiation. He do he derived is in linear is gravity, he derived his 34 00:06:00,510 --> 00:06:18,900 Maciej Kolanowski: Quadruple formula. And then there were literally decades of work on this topic and also the Seekers solution to answer any questions is one of the oldest oceans ever found. So one could think that we should understand right now, everything about it. 35 00:06:19,200 --> 00:06:27,510 Maciej Kolanowski: But unfortunately, it's not true because apparently those two topics are not exactly compatible. 36 00:06:29,400 --> 00:06:31,170 Maciej Kolanowski: And because as 37 00:06:32,310 --> 00:06:53,130 Maciej Kolanowski: Usually when we think about radiation. For example, in a course on electrodynamics, we say that radiation, something that an observer at infinity can see. So this infinity in the sitter universe is totally different than in demean coughs Q1. 38 00:06:54,270 --> 00:07:00,060 Maciej Kolanowski: Because in Assam politically flat space times infinity on the which 39 00:07:01,500 --> 00:07:02,520 Maciej Kolanowski: One measures. 40 00:07:02,790 --> 00:07:04,680 Maciej Kolanowski: Edition is now infinitely 41 00:07:06,300 --> 00:07:17,040 Maciej Kolanowski: Worse. In this case, as you can see from this over 10 rows diagram and cry is actually space like 42 00:07:18,330 --> 00:07:28,620 Maciej Kolanowski: So it changes everything because all those decades of work of Troutman and Bondi and Zach's and Iranian pencils and so on. 43 00:07:29,100 --> 00:07:54,240 Maciej Kolanowski: It was what in for us in particular that space times with now sky, which is equipped with at tone of universal structures. So you have universal metric in youth on this cry and you have BMS group and now everything is lost, and we need to start from scratch. 44 00:07:56,040 --> 00:08:06,390 Maciej Kolanowski: Moreover, it is natural to define energy as something connected with some killing vector as some density 45 00:08:08,790 --> 00:08:30,390 Maciej Kolanowski: Some charts of a killing vector, but here in this case all vectors tangent prescribed so all King vectors are spaceflight be because the sky is a space like so it means that the charges could be either positive or negative. And they could be actually arbitrary negative 46 00:08:32,850 --> 00:08:59,580 Maciej Kolanowski: Is so we don't have any. And so we could a priori have negative energy, which seems kinda it is disturbing because we think about energy even even this very small energy of gravitational waves we can detect as some physical thing that we could use for example to warm up a cup of tea. 47 00:09:00,900 --> 00:09:11,730 Maciej Kolanowski: And here apparently there is a risk that if and if the genre additions calm then actually our T is going to be colder instead of warmer. 48 00:09:13,470 --> 00:09:14,610 Maciej Kolanowski: And more over 49 00:09:15,900 --> 00:09:23,520 Maciej Kolanowski: Anybody if if we have some physical observer and you were then he or she cannot 50 00:09:24,810 --> 00:09:30,180 Maciej Kolanowski: See everything in the universe, and they are bounded by the cosmological horizon. 51 00:09:31,500 --> 00:09:40,980 Maciej Kolanowski: So we that another issue is something different that we are not able to see everything on the part of our universe. 52 00:09:43,050 --> 00:09:52,560 Maciej Kolanowski: And last but not least, there is also a thing called just noun for 60s 60s, I think, which is called the origin problem. 53 00:09:53,970 --> 00:10:00,210 Maciej Kolanowski: Usually when you describe radiation, either in electrodynamics on in 54 00:10:01,800 --> 00:10:19,260 Maciej Kolanowski: On linear is gravity. You start with someone over enter our expansion and I differ identify appropriate term as radiation. And then you say that some higher order times in one of our, our ARE NOT A NATION bar code on big mode. 55 00:10:20,160 --> 00:10:40,410 Maciej Kolanowski: But unfortunately it was pointed out in 60s by Penrose that you, you cannot do this in a reasonable way on the decision if you have cosmological concept of any sign either plus or minus 56 00:10:42,240 --> 00:10:51,690 Maciej Kolanowski: And because then it is dependent on the region around which you have this are coordinate 57 00:10:52,350 --> 00:11:11,790 Maciej Kolanowski: In the inverse of which you expand. So if you move your origin as we actually seen and later on in this topic in the stock if you move the origin, you mix radiative and Colombia modes and you also mix their energies, even at their level of linear is the gravity. 58 00:11:15,300 --> 00:11:18,480 Maciej Kolanowski: Oh, last but not least, it's the question of 59 00:11:20,550 --> 00:11:32,550 Maciej Kolanowski: The second last but not least, is the question of boundary conditions, one should impose. So for example, in a DS. You can impose at infinity. 60 00:11:33,240 --> 00:11:50,190 Maciej Kolanowski: Reflective boundary conditions which simply means that magnetic part. Leading. Leading order magnetic part of the violence or vanishes and the boundary. But here you as well. Sean, I think I should buy those outdoors, you cannot 61 00:11:51,900 --> 00:12:00,240 Maciej Kolanowski: Put any such restriction and on vital tensile, you need to work with the whole object both electric and magnetic 62 00:12:00,270 --> 00:12:00,660 Maciej Kolanowski: Part 63 00:12:00,690 --> 00:12:01,320 It's crazy. 64 00:12:04,080 --> 00:12:06,570 Maciej Kolanowski: Excuse me. Was that the question or 65 00:12:09,870 --> 00:12:10,980 Seth K Asante: Better. Yeah. 66 00:12:13,830 --> 00:12:14,430 Jorge Pullin: No, go ahead. 67 00:12:15,240 --> 00:12:15,960 Maciej Kolanowski: OK. OK. 68 00:12:18,210 --> 00:12:19,140 Maciej Kolanowski: So moving on. 69 00:12:20,700 --> 00:12:30,060 Maciej Kolanowski: And there was a lot of activity in this topic in the last few years. So there were different proposals of energy. 70 00:12:31,260 --> 00:12:37,980 Maciej Kolanowski: And and using different formulas and also different proposal of boundary conditions, different 71 00:12:39,960 --> 00:12:45,060 Maciej Kolanowski: Gauge choices which were supposed to be better or worse for whatever 72 00:12:46,920 --> 00:12:51,630 Maciej Kolanowski: And then finally, some people actually remember that they should be 73 00:12:54,270 --> 00:13:03,060 Maciej Kolanowski: Up and that they should be doing physics and applied this formalism to some physical astrophysical say astrophysical situations. 74 00:13:03,870 --> 00:13:20,730 Maciej Kolanowski: And so here's the good news. Good news is that we are not going to propose a new definition. So we believe that a number of proposal is enough, who are going to work and with what those people 75 00:13:21,870 --> 00:13:25,440 Maciej Kolanowski: Need to appear with what 76 00:13:28,950 --> 00:13:49,830 Maciej Kolanowski: Those people proposed and also. And recently, a few months ago also proposal by Khrushchev Haka and smoker. And so we want to combine as simplistic formalities of our sticker bongha and cassava with 77 00:13:52,080 --> 00:13:57,360 Maciej Kolanowski: With light cone and definitions of energy of who show hawk and smoker and 78 00:13:58,530 --> 00:14:02,790 Maciej Kolanowski: Let us see, where can we get, what can we get from this 79 00:14:05,100 --> 00:14:05,580 Maciej Kolanowski: Okay. 80 00:14:13,860 --> 00:14:15,150 Maciej Kolanowski: Okay, and 81 00:14:17,100 --> 00:14:18,720 Maciej Kolanowski: So what is our strategy. 82 00:14:19,800 --> 00:14:27,960 Maciej Kolanowski: We start with the sitter universe, who would she can all see here and we're going to Linares gravity around it. 83 00:14:29,490 --> 00:14:37,530 Maciej Kolanowski: So it's very preliminary thing at something and Einstein did more than 100 years ago. 84 00:14:38,910 --> 00:14:52,740 Maciej Kolanowski: So it's not very and but we are still not really able to do anything interesting at the nonlinear level. So it is Wakefield approximation first time. 85 00:14:54,390 --> 00:14:58,260 Maciej Kolanowski: We work with those so called burden coordinates, because 86 00:14:58,800 --> 00:15:11,400 Maciej Kolanowski: There's worse suited for taking a min costs can limit, as you can see when lambda goes to zero, we simply good mink of system. It's nice and those coordinates are well defined. 87 00:15:11,880 --> 00:15:27,690 Maciej Kolanowski: And also because they were surprisingly well at scribe, of course, using appropriate as you're using appropriate confirm or factor, which in our case is given by 88 00:15:33,510 --> 00:15:37,200 Maciej Kolanowski: And Hubble constants minus one times are 89 00:15:38,460 --> 00:15:38,730 Maciej Kolanowski: Healthy 90 00:15:39,990 --> 00:15:51,570 Maciej Kolanowski: And I'm going to use frequently Hubble Constant in the case of the sitter. It's simply square root of lambda over free 91 00:15:54,630 --> 00:16:03,300 Maciej Kolanowski: And okay so this will be useful, and we want to define our charges of the digital group just as 92 00:16:04,530 --> 00:16:11,400 Maciej Kolanowski: A speaker mongan seven did using simplicity definitions and actually 93 00:16:12,120 --> 00:16:23,970 Maciej Kolanowski: Everybody knows that those definitions are and nice and up to boundary terms. And of course, if you're interested in the whole charge at those bundy terms should not contribute. So it doesn't matter. 94 00:16:24,570 --> 00:16:39,810 Maciej Kolanowski: And bad if you are, if you want to derive something like Feldman Bondi Maslow's formula then you actually care about and bank details. So our strategy is 95 00:16:41,190 --> 00:16:55,320 Maciej Kolanowski: As such, and that we don't care right now about bank details we simply ignore them and we wanted to fix them somehow by some other methods at the end of our calculations. 96 00:16:56,310 --> 00:17:12,720 Maciej Kolanowski: And show that our result is the only one which which has the following nice properties. And this is why those boundary terms are. I'm the way they are. And so 97 00:17:14,280 --> 00:17:15,330 Maciej Kolanowski: I mentioned already, 98 00:17:15,330 --> 00:17:28,770 Maciej Kolanowski: This paper from this year by who's Jehovah and smoker, in which they were very careful in deriving boundary towels and only to find out at the end that 99 00:17:29,220 --> 00:17:42,600 Maciej Kolanowski: Those bandy terms and produce some infinities which they need to regularize. So, which basically means that they needed to change somehow a talk. 100 00:17:43,980 --> 00:17:57,030 Maciej Kolanowski: Those bandy terms. They just the right so we decided that it doesn't seem like fun, and we we just don't care about Mandy terms at the spot. 101 00:17:59,100 --> 00:18:03,600 Abhay Ashtekar: And ask question. I mean, is your control factor correct or is it the inverse of the confounding factor. 102 00:18:09,240 --> 00:18:12,630 Abhay Ashtekar: I think a confounding factors should go to is blows up at infinity. 103 00:18:13,920 --> 00:18:17,850 Maciej Kolanowski: Excuse me, I have. Okay, so this is confirming factor. 104 00:18:20,070 --> 00:18:24,300 Maciej Kolanowski: Come from our factor is at times are 105 00:18:25,470 --> 00:18:25,740 Maciej Kolanowski: Okay. 106 00:18:25,770 --> 00:18:27,240 Abhay Ashtekar: So, it blows up at infinity. 107 00:18:29,220 --> 00:18:31,050 Maciej Kolanowski: Okay, so I can put minus one. 108 00:18:34,230 --> 00:18:34,560 Abhay Ashtekar: Minus 109 00:18:34,830 --> 00:18:39,570 Maciej Kolanowski: Good. Yes, there was also another minus one missing. Thank you. 110 00:18:43,080 --> 00:18:57,690 Maciej Kolanowski: Oh, and actually we use this definition of conformal factor because and now it's dimension less and metric induced on Sky has proper has the same dimension as the metric. We start 111 00:19:00,270 --> 00:19:00,840 Maciej Kolanowski: Okay. 112 00:19:06,270 --> 00:19:07,380 Maciej Kolanowski: So, let us move on. 113 00:19:08,430 --> 00:19:24,690 Maciej Kolanowski: So we have a killing vector of the decider universe, and we can define a chart of line calm using the following formula formula, as I said, it's well defined up to boundary charge up to boundary terms and we hope. 114 00:19:28,200 --> 00:19:32,400 Maciej Kolanowski: We hope that we would need to care about them right now. 115 00:19:35,460 --> 00:19:36,180 Maciej Kolanowski: Okay. 116 00:19:40,020 --> 00:20:00,360 Maciej Kolanowski: As I said, we need to establish boundary terms later on I will focus mainly on the decider G which is simply given by this vector d up and do you because as you could see, as you can see here, this vector becomes a time 117 00:20:02,040 --> 00:20:08,100 Maciej Kolanowski: Generator of time translation when lambda goes to do so is the most natural choice. 118 00:20:12,330 --> 00:20:21,510 Maciej Kolanowski: Okay. And so this is an area of the one of one calm and our plan is following. We can fall. Yay. 119 00:20:23,670 --> 00:20:29,040 Maciej Kolanowski: At least part of this faith in by light comes emitted from a single line so we 120 00:20:30,780 --> 00:20:36,750 Maciej Kolanowski: We have a line and we have different now comes emitted from this 121 00:20:38,310 --> 00:20:41,580 Maciej Kolanowski: And we can calculate and their gene. 122 00:20:42,750 --> 00:20:46,320 Maciej Kolanowski: In each now calm and copper them. 123 00:20:48,210 --> 00:20:53,190 Maciej Kolanowski: Of course we should introduce some cut off. So let's say that we have 124 00:20:54,240 --> 00:20:59,040 Maciej Kolanowski: It looks like this. And we on the integrate up to some 125 00:21:00,300 --> 00:21:15,000 Maciej Kolanowski: Some are. And then when we go with our to infinity, we should obtain difference of energies but when to infinity. Now cons, which would identify with. 126 00:21:16,620 --> 00:21:19,770 Maciej Kolanowski: And then emitted by the system. 127 00:21:21,030 --> 00:21:28,920 Maciej Kolanowski: Here, this, this picture is kind of misleading because it seems to those are surfaces are equal constants 128 00:21:31,890 --> 00:21:57,930 Maciej Kolanowski: And it seemed that their timeline, but in fact it. But in fact, the correct answer would be that it depends. As you can again see from this metric, if you have some if our small, then those surfaces, our timeline at are equal equal one of our Hubble Constant and it is 129 00:21:59,130 --> 00:22:03,480 Maciej Kolanowski: Now surface. In fact, it is a cosmological horizon and 130 00:22:05,190 --> 00:22:05,910 Maciej Kolanowski: And the future. 131 00:22:06,930 --> 00:22:15,390 Maciej Kolanowski: Magical horizon. And then when we go with our to infinity. It's going to be space like and this space like surface in the limit becomes cry. 132 00:22:17,040 --> 00:22:18,840 Maciej Kolanowski: Okay, so let me know. 133 00:22:27,330 --> 00:22:28,260 Maciej Kolanowski: And move on. 134 00:22:30,030 --> 00:22:47,610 Maciej Kolanowski: Okay, so that was our strategy and now we need to make it happen. So obviously we need to introduce them gage some expand some boundary conditions at infinity. And so we use Bondi 135 00:22:49,980 --> 00:22:52,410 Maciej Kolanowski: And gauge and assume the following 136 00:22:52,950 --> 00:23:00,060 Maciej Kolanowski: Some topics as our excuse me, it's obviously a typo here it's are going to infinity. 137 00:23:04,110 --> 00:23:04,380 Maciej Kolanowski: Okay. 138 00:23:05,610 --> 00:23:07,650 Maciej Kolanowski: We assume the following as competitive. 139 00:23:10,020 --> 00:23:13,410 Maciej Kolanowski: And and those boundary conditions here. 140 00:23:15,030 --> 00:23:19,470 Maciej Kolanowski: As you can see, and there's no one over r squared term here. 141 00:23:21,270 --> 00:23:43,980 Maciej Kolanowski: And because it zero and it follows ultimate in the case of positive cosmological constant, a fact that this term is zero flows automatically from Einstein equations, assuming the to have smooth structure as described it's it was shown, I think by Friday in 80s. 142 00:23:46,890 --> 00:23:59,730 Maciej Kolanowski: And by contrast in synthetically flood space time you all you have the term and it produces some logarithmic corrections, but they are totally missing in 143 00:24:01,320 --> 00:24:02,820 Maciej Kolanowski: One lump that lambda is positive. 144 00:24:08,340 --> 00:24:09,420 Maciej Kolanowski: And 145 00:24:11,010 --> 00:24:17,940 Maciej Kolanowski: The two main differences between us, in particular space times are such that this age zero is not zero. 146 00:24:19,470 --> 00:24:22,950 Maciej Kolanowski: Although, as we'll see, it is of order. 147 00:24:24,540 --> 00:24:26,640 Maciej Kolanowski: Lambda for small lambda 148 00:24:30,120 --> 00:24:45,930 Maciej Kolanowski: And more over tense those terms here are free data which needs to satisfy some constraints at scribe bought, but we can prescribe them. They are not 149 00:24:49,350 --> 00:24:56,880 Maciej Kolanowski: Yeah. And so our free data here are actually this A H zero and those terms you 150 00:24:58,650 --> 00:25:03,420 Maciej Kolanowski: H minus one and here it is actually 151 00:25:04,770 --> 00:25:07,560 Maciej Kolanowski: And it's actually determined by h zero 152 00:25:11,580 --> 00:25:14,640 Maciej Kolanowski: And this is kind of strange choice of 153 00:25:15,930 --> 00:25:29,640 Maciej Kolanowski: Gauge because usually, I think that people work with so called radio gauge in which you know which H. A. Your starts with minus one and a HIV starts with zero 154 00:25:30,150 --> 00:25:48,150 Maciej Kolanowski: We decided on this gauge, simply because who show kaka and smoke at it and they they chose this gauge because their expressions. Well, we're less divergent using this gauge. Then there are the radar one 155 00:25:51,840 --> 00:25:55,740 Maciej Kolanowski: And and we wanted to compare our results to theirs. 156 00:25:58,410 --> 00:25:59,460 Maciej Kolanowski: Okay, so 157 00:26:01,200 --> 00:26:08,790 Maciej Kolanowski: Those are our assumptions around infinity and let us calculate and this energy emitted. 158 00:26:11,250 --> 00:26:18,360 Maciej Kolanowski: It's kind of tedious calculation. But at the end of the day, using Stokes Durham. Obviously, up in the following 159 00:26:19,800 --> 00:26:20,490 Maciej Kolanowski: Expression. 160 00:26:22,590 --> 00:26:41,760 Maciej Kolanowski: And no natural quick, let me let me emphasize that this is energy emitted between two now cons, not necessarily infinite. Infinite times. So it means that we have really energy emitted during some finite period of time. 161 00:26:43,140 --> 00:26:50,970 Maciej Kolanowski: And we have some boundary terms to which simply come from our definitions. The question is whether we should discard them. 162 00:26:52,020 --> 00:26:54,090 Maciej Kolanowski: Well, we definitely should defer 163 00:26:56,070 --> 00:27:00,510 Maciej Kolanowski: This plan because it's always the limit lambda goes to zero. 164 00:27:02,640 --> 00:27:25,830 Maciej Kolanowski: If we discard this term which simply means that we added to the definition of the energy or with with opposite sign we added to the definition of energy of anelka little 50 correct lambda zero limits, but we have this them and it's not obvious, whether we should also discard it or not. 165 00:27:28,560 --> 00:27:35,370 Maciej Kolanowski: So because it actually goes to zero as as as lambda goes to zero. 166 00:27:37,260 --> 00:27:52,440 Maciej Kolanowski: So it doesn't matter in the limit. So we are going to, as we mentioned in our strategy, we just don't care about branded terms. So we discard it. And we perhaps we will restart. Later on, we'll see. 167 00:27:54,300 --> 00:27:55,590 Abhay Ashtekar: What is gamma not 168 00:27:57,840 --> 00:28:01,620 Maciej Kolanowski: A gamma not is metric on a unit spirit. 169 00:28:03,180 --> 00:28:07,980 Abhay Ashtekar: Okay, so it is it there's no automated just magically 170 00:28:09,150 --> 00:28:19,500 Maciej Kolanowski: Because those are the coefficients in one over our expansion, so it is somehow already. This is as our goes to zero, it goes to infinity. 171 00:28:20,850 --> 00:28:22,380 Maciej Kolanowski: And there's a need 172 00:28:23,430 --> 00:28:24,720 Maciej Kolanowski: And now come 173 00:28:26,460 --> 00:28:26,820 Abhay Ashtekar: Thank you. 174 00:28:28,590 --> 00:28:31,770 Maciej Kolanowski: Thank you for the question. And also that let 175 00:28:31,800 --> 00:28:32,850 Abhay Ashtekar: Me mention that for the 176 00:28:32,850 --> 00:28:33,900 Maciej Kolanowski: Future use so 177 00:28:34,980 --> 00:28:41,490 Maciej Kolanowski: The whole immediate energy. We're going to call duty, because, well, after all, it is a chart. 178 00:28:47,070 --> 00:28:57,570 Maciej Kolanowski: Okay, by in the same way we could define radiated angular momentum, either from the minus two plus infinity or for some 179 00:28:59,580 --> 00:29:01,320 Maciej Kolanowski: For some finite 180 00:29:05,160 --> 00:29:07,320 Maciej Kolanowski: Oh, I think I have a question on top. 181 00:29:16,860 --> 00:29:17,520 Maciej Kolanowski: Oh, 182 00:29:20,280 --> 00:29:23,880 Maciej Kolanowski: Yeah, it can we discuss it later on. 183 00:29:27,300 --> 00:29:27,720 Jorge Pullin: Good. 184 00:29:28,380 --> 00:29:31,800 Maciej Kolanowski: Because he is definitely there is the connection. Okay, great. Thank you. 185 00:29:35,700 --> 00:29:45,930 Maciej Kolanowski: And as I said, we could also and design eradicated angular momentum, either at finite or infinite 186 00:29:47,790 --> 00:29:48,210 Maciej Kolanowski: Time. 187 00:29:49,470 --> 00:29:55,290 Maciej Kolanowski: We could also define and spatial momentum, but it was 188 00:29:55,320 --> 00:29:57,180 Maciej Kolanowski: Actually too complicated for us. 189 00:29:57,510 --> 00:30:00,060 Maciej Kolanowski: And we're somehow not able to 190 00:30:01,080 --> 00:30:14,730 Maciej Kolanowski: To produce finance limited because there was a lot of terms which should cancel on on the show, but there's too many of them so will derive this charge in a different manner. 191 00:30:18,690 --> 00:30:23,640 Maciej Kolanowski: Okay, as I mentioned in the introduction, and 192 00:30:26,760 --> 00:30:28,650 Abhay Ashtekar: Because we're going to the next topic now. 193 00:30:30,510 --> 00:30:33,540 Maciej Kolanowski: I'm not. It's still about this term just said infinity. 194 00:30:34,170 --> 00:30:41,730 Abhay Ashtekar: Okay, but I still this white answer now so I'm just understanding the phone if you can go back to your Penrose diagram on page five 195 00:30:44,010 --> 00:30:51,990 Abhay Ashtekar: And just, I think it looks wrong. Yeah. Yeah. Yeah, about that vendors like I'm just draw what you're doing. 196 00:30:53,550 --> 00:31:01,470 Abhay Ashtekar: Yet I I do look at the left hand straight line and two points on it and light comes going from there. Yeah. Can you draw the light codes. 197 00:31:05,250 --> 00:31:06,390 Maciej Kolanowski: It's of course 198 00:31:08,010 --> 00:31:08,370 Abhay Ashtekar: Yes. 199 00:31:08,490 --> 00:31:14,190 Maciej Kolanowski: Thank you. We we calculate flux actually density not flux at this part. 200 00:31:14,910 --> 00:31:15,300 Yeah. 201 00:31:16,380 --> 00:31:16,770 Abhay Ashtekar: Thank you. 202 00:31:30,810 --> 00:31:39,600 Maciej Kolanowski: Okay, so you mentioned actually at the spindle diagram. It is natural to consider violence or 203 00:31:40,830 --> 00:31:42,330 Maciej Kolanowski: Its cry so 204 00:31:43,980 --> 00:31:58,290 Maciej Kolanowski: We introduced it's electric part. And of course, of the linear eyes advice answer and and to one contract that it vanishes as our goes to infinity. So, we 205 00:31:59,730 --> 00:32:09,780 Maciej Kolanowski: Just want to correct. And so we can introduce rescheduled electric part of the winner is vital. So, simply by multiplying by 206 00:32:10,530 --> 00:32:15,900 Maciej Kolanowski: One over confirm the factor. And then the limit a particular one contract. 207 00:32:16,200 --> 00:32:17,730 Maciej Kolanowski: That this is 208 00:32:18,420 --> 00:32:20,640 Maciej Kolanowski: All one get from the definition 209 00:32:23,130 --> 00:32:39,450 Maciej Kolanowski: And okay, why does it matter. It matters because we can rewrite our charges use those are now those charges between minus and plus infinity using those two equations. 210 00:32:41,820 --> 00:32:51,780 Maciej Kolanowski: And we obtain the following very nice form and this h minus two is because and the 211 00:32:53,730 --> 00:33:05,700 Maciej Kolanowski: Metric induced by perturbation on Sky is not actually a zero but public Constance minus two times ages zero. So here it is actually 212 00:33:09,660 --> 00:33:12,030 Maciej Kolanowski: Um, this is metric 213 00:33:20,280 --> 00:33:22,050 Maciej Kolanowski: Metric induced unsubscribe. 214 00:33:25,140 --> 00:33:36,750 Maciej Kolanowski: And they look surprisingly similar to once obtained before and Professor ash Tucker and his guru. Namely, we have 215 00:33:38,040 --> 00:33:38,310 Maciej Kolanowski: So, 216 00:33:40,200 --> 00:33:52,590 Maciej Kolanowski: This is, this is the result. You can see some differences. A letter P here stands for one correct because they calculated in in Concord. 217 00:33:55,230 --> 00:33:56,760 Maciej Kolanowski: And you can check 218 00:33:58,590 --> 00:34:03,450 Maciej Kolanowski: Okay I think now, and you can check that by 219 00:34:04,620 --> 00:34:25,500 Maciej Kolanowski: That if you perform the following come from a transformation from the data and defined in the pond carapace to the data in the sky, Allah Bondi you obtain exactly and lower result of course for time translation and for angular momentum. 220 00:34:29,340 --> 00:34:33,330 Maciej Kolanowski: And. Okay. And so, it suggests that 221 00:34:34,350 --> 00:34:44,250 Maciej Kolanowski: This that also momentum should should be obtained by such a transformation. And then in our annotation. It looks like this. 222 00:34:45,450 --> 00:34:53,190 Maciej Kolanowski: And a translation generator in Bondi gauges. It's not very nice. It is given by equation. 223 00:34:55,470 --> 00:35:08,220 Maciej Kolanowski: And of course all boundary can which we could derive from some cryptic formulation are totally lost because those expressions here are our global expressions. 224 00:35:12,450 --> 00:35:17,520 Maciej Kolanowski: Okay. So we see that we have some sort of compatibility 225 00:35:18,780 --> 00:35:28,350 Maciej Kolanowski: Compatibility and between reviews results previously found in the literature and this nice and let us 226 00:35:31,020 --> 00:35:37,680 Maciej Kolanowski: But what are perhaps some differences. So you can check what kind of data is 227 00:35:40,140 --> 00:35:52,770 Maciej Kolanowski: What kind of data and in those a BK charges are allowed, and you have some smoothness conditions at at the origin of your scribe 228 00:35:53,370 --> 00:36:13,020 Maciej Kolanowski: Which translates into the following conditions in our gauge as you goes to infinity that this metric induced on Sky goes to a constant plus some exponentially small terms and electric part of the right answer should vanish exponentially. 229 00:36:14,940 --> 00:36:23,100 Maciej Kolanowski: But actual we can check that we don't need such strict boundary conditions as you go through minus a plus infinity. 230 00:36:24,150 --> 00:36:38,490 Maciej Kolanowski: To have final energy. We only need that electric part of the very tense or is constant and then it is a little bit stronger condition to have finite angular momentum and to have finite 231 00:36:40,530 --> 00:36:55,260 Maciej Kolanowski: To have finite a spatial momento, it kind of stronger, but still, it's much weaker come it is still a weaker condition, then the one obtained in the quantity 232 00:36:57,090 --> 00:37:02,310 Maciej Kolanowski: And let us also note that should what should the sitter is actually what in the first category. 233 00:37:03,090 --> 00:37:24,870 Maciej Kolanowski: Of those, but it has finally old charges because sometimes it cancels out. So perhaps it is possible that even somehow we care about the conditions are needed. This is and this is the easiest the version one can get it simply by looking at formulas and require that they're finally 234 00:37:26,190 --> 00:37:38,670 Abhay Ashtekar: I guess or to say some couple things. First of all, you call him Uncle patches okay with me, but it's slightly misleading because you're also working upon correct patch. That's why I STARTED TO LOOK AT THE LOOK AT THE Penrose diagram. 235 00:37:39,840 --> 00:37:45,360 Abhay Ashtekar: All you know khonsari within that one correct patch. I think so. The difference is really that we are using 236 00:37:46,380 --> 00:37:46,800 Abhay Ashtekar: Kind of 237 00:37:48,120 --> 00:37:56,250 Abhay Ashtekar: Cosmological coordinates adapted to conquer a patch, whereas you're using the Bondi coordinates. Is that correct, that is a difference. You're talking about 238 00:37:57,000 --> 00:37:57,990 Maciej Kolanowski: Yes, indeed. 239 00:37:58,650 --> 00:38:07,170 Abhay Ashtekar: But OK, then I think that if I just actually solve the linear equations in the 240 00:38:08,310 --> 00:38:19,860 Abhay Ashtekar: Spawn carry patch, then the fall off that we assume is the fall of you get from solutions. So you might assume Lord follow up, that's fine, but the solutions actually on the sitter. 241 00:38:20,520 --> 00:38:38,040 Abhay Ashtekar: Will have the fall of that we assume we give the solutions explicitly. I mean, it's not as many other people that I worked on this already. So I just wanted to point out that the assumption that we get made was really based on the exquisite fall of the solutions themselves. 242 00:38:39,270 --> 00:38:40,830 Maciej Kolanowski: And yes, sure. 243 00:38:42,900 --> 00:38:52,320 Maciej Kolanowski: I totally agree with in this comparison, will we rather had in mind some next thing, one could make so introduce actually some black 244 00:38:54,540 --> 00:39:01,650 Maciej Kolanowski: I don't know. What about fall off of because I think you also derived solutions from 245 00:39:02,790 --> 00:39:08,820 Maciej Kolanowski: From the source. Do they also have the same decay is 246 00:39:08,880 --> 00:39:11,040 Maciej Kolanowski: The CNN. Okay. Oh. 247 00:39:11,070 --> 00:39:25,050 Abhay Ashtekar: Yes, yes. I think that was that was that something that follows from the Greens function that other people have actually calculated before. Yeah, okay. But I just want to clarify this so that I'm sure that I'm not missing something. Thank you very much for you. 248 00:39:29,040 --> 00:39:29,490 Maciej Kolanowski: Know, 249 00:39:31,170 --> 00:39:42,150 Maciej Kolanowski: Okay, I mentioned a few times that we want to fix somehow boundary conditions, and we are going to do this by imposing some sort of gauge invariance. 250 00:39:42,630 --> 00:39:53,520 Maciej Kolanowski: And he transformations are those are somehow large gauge transformations, because they act action inscribed on the initial data can act as falls in 18 and 251 00:39:54,120 --> 00:40:04,170 Maciej Kolanowski: 19 and actually not all, we're still missing some large image transformations, but it doesn't make any difference in what I'm going to say 252 00:40:05,610 --> 00:40:15,660 Maciej Kolanowski: Since the sitter is confirming flat, it's very tense or is going to always to be engaged independent so it doesn't transform at all. 253 00:40:16,980 --> 00:40:32,040 Maciej Kolanowski: Okay, using those we can calculate how this difference of energy changes. Okay, we obtained such expression and to check that actually there are no boundary terms which would be an and 254 00:40:32,640 --> 00:40:46,350 Maciej Kolanowski: Try linear in in violence or in metric in use. And in this attack vector, which would killed this entirely so you cannot actually demand that it is totally 255 00:40:47,460 --> 00:40:54,420 Maciej Kolanowski: gauging very despite the fact that this expression is very nice geometrically and but we can make something 256 00:40:57,240 --> 00:41:11,400 Maciej Kolanowski: We should establish at least the residual gauge transformations which do not change our initial choices. So they're of this form, it's not very nice and 257 00:41:14,520 --> 00:41:19,980 Maciej Kolanowski: And okay, and there's still too many of them because they are parameters by one 258 00:41:20,490 --> 00:41:36,180 Maciej Kolanowski: Function on a spirit which is you independent and also by you dependent confirm are killing vectors. So it's definitely too many of them, we need to, but it was proposed how to kill at least partially this gauge freedom. 259 00:41:37,260 --> 00:41:46,920 Maciej Kolanowski: We can impose some additional gauge condition and which roughly speaking, means that cones do not rotate with respect to each other. 260 00:41:47,670 --> 00:42:01,680 Maciej Kolanowski: And and as a result we opt in, much simpler as a jewel gauge transformations mainly only those generated by dysfunction on a sphere which is you independent plus killing vectors of the whole met 261 00:42:02,190 --> 00:42:10,950 Maciej Kolanowski: But obviously clean vectors of the whole metric at the gallery on PR to native data so they can change it and those 262 00:42:12,540 --> 00:42:17,160 Maciej Kolanowski: a gauge transformation is generated by this function and 263 00:42:18,180 --> 00:42:20,580 Maciej Kolanowski: Also, does not change our energy loss formula. 264 00:42:22,830 --> 00:42:45,270 Maciej Kolanowski: Okay, and now it would be tempting to call such a residual gauge transformations super translations, because they look exactly the same as in the case of lambda in assembly in BMS group, but I think it's a misnomer because spatial translations are not have this form. 265 00:42:46,350 --> 00:43:09,000 Maciej Kolanowski: So we decided to go for much catch your name there, namely super pseudo translations and let us also know that they do not commute and we're killing vectors of our metric just actually just as in the case of mean cosmetic when it is a source for them. 266 00:43:10,200 --> 00:43:11,670 Maciej Kolanowski: Angular momentum problem. 267 00:43:13,530 --> 00:43:18,990 Maciej Kolanowski: Okay, so we have different muscles formula without any bounded tense whatsoever. 268 00:43:19,530 --> 00:43:35,670 Maciej Kolanowski: And which is the only expression which has the correct correct lambda to go to zero limit. And there's also invariant with with respect to all super pseudo translations. So it is a difference, I think, and 269 00:43:36,480 --> 00:44:00,060 Maciej Kolanowski: And physical result as a result in this presentation. And this was also obtained by the means of network CRM and by kusa Hawkins smoker, but then they had some ad hoc regularization, and now we understand that this this way of regular rising was justified exactly by gauging variance 270 00:44:02,220 --> 00:44:14,940 Maciej Kolanowski: Okay, so what we could also do we could try to drive us formula for the rest of charges but then they do not Camille killing vector do not commit with super translations. 271 00:44:15,780 --> 00:44:25,470 Maciej Kolanowski: We could ask about non small cry and there are some solutions, actually. And we could also generalize it to the nonlinear theory. 272 00:44:27,060 --> 00:44:44,190 Maciej Kolanowski: And then it's hard to mention a super translations and not also mentioned stuff to get it done. So it is natural, natural question whether we have some soft modes here. And what does it actually mean. And since we have totally different boundary conditions for our 273 00:44:46,170 --> 00:44:47,640 Maciej Kolanowski: For our as metrics. 274 00:44:49,050 --> 00:45:10,020 Maciej Kolanowski: Okay, so it is different. It was the first part of our talk. The second part is, is concerned with the horizon, you only work with flux, it will to calculate it again in Bondi coordinates in Bondi gauge. It's not very nice expression. As you can see, 275 00:45:14,550 --> 00:45:23,760 Maciej Kolanowski: But let us try to check what is going on in the limit as lambda goes to zero. So we have the following expansion of our fields. 276 00:45:25,200 --> 00:45:36,870 Maciej Kolanowski: And so it might seem that going with lambda zero is like going to with our to infinity. So then this term would be 277 00:45:41,280 --> 00:45:42,060 Maciej Kolanowski: So then 278 00:45:43,830 --> 00:45:48,270 Maciej Kolanowski: This time time would be dominating, but it is actually not the case. 279 00:45:50,880 --> 00:46:15,540 Maciej Kolanowski: And because all those coefficients can also depend upon lambda. And in fact, when we go with lambda zero we have that H zero is proportional to lambda, whereas H A B minus one is a constant. Hmm. So we should also include this in our limiting procedure. 280 00:46:18,090 --> 00:46:18,480 Maciej Kolanowski: And 281 00:46:19,620 --> 00:46:25,200 Maciej Kolanowski: And then you can check that, in fact, the only term that contribute is 282 00:46:27,840 --> 00:46:28,410 Maciej Kolanowski: This term. 283 00:46:30,630 --> 00:46:32,820 Maciej Kolanowski: Which which happened to be 284 00:46:34,440 --> 00:46:34,860 Maciej Kolanowski: Done. 285 00:46:36,180 --> 00:46:48,570 Maciej Kolanowski: So in the limit on it this time contribute and this thermal exactly again reproduces flocks of the energy Angelina is gravity. 286 00:46:49,980 --> 00:46:57,750 Maciej Kolanowski: In a simplistic this flat space times. And again, we have some boundary terms which one should should fix somehow 287 00:47:03,960 --> 00:47:14,160 Maciej Kolanowski: It. Okay. So as I mentioned, it is not a simple large our expansion because also somehow coefficients also depend upon it. 288 00:47:15,300 --> 00:47:30,300 Maciej Kolanowski: And the leading form of those coefficients Islam that goes to zero, is as follows. This that HIV goes to infinity as it should actually and HIV goes to a constant, constant again as it should in mink of suspects. 289 00:47:34,500 --> 00:47:41,460 Maciej Kolanowski: Okay. And again, we have some open questions. First of all, can we show this on the horizon. So 290 00:47:42,180 --> 00:47:55,620 Maciej Kolanowski: Because here to show this limit we needed to use some additional structure for from scribe. So it's kind of like cheating, could we make it interesting and then 291 00:47:56,430 --> 00:48:10,140 Maciej Kolanowski: There's a question about our assumption because evidently we assumed and that radius of convergence in this one of our expansions reaches cosmological horizon and 292 00:48:10,800 --> 00:48:26,100 Maciej Kolanowski: Is it true, and also we somehow expand coefficients in lambda. So then the question would be whether this expansion is also convergent, in some sense, or our adult those only formal 293 00:48:28,890 --> 00:48:36,150 Maciej Kolanowski: Formal writings and then again. And this question of what happens in the non Smith's at an unsubscribe. 294 00:48:36,990 --> 00:48:48,330 Maciej Kolanowski: And because when lambda is going. It's positive and this notion of structure at Sky is totally different much more complicated than India simplistically flat space time 295 00:48:48,570 --> 00:49:09,870 Maciej Kolanowski: When it is simply logarithmic term. So it would, I think it would be also interesting to check what's going on at the horizon, whether we have some logarithmic term or something different when we have some sort of neurons movements and what one would also think, what does it mean, actually. 296 00:49:11,940 --> 00:49:27,900 Maciej Kolanowski: And again, this is only the whole flux and not mass loss formula and can one could ask whether we can use the same argument will use before to fix bounded terms and it's somehow 297 00:49:28,260 --> 00:49:36,180 Maciej Kolanowski: Hard because differently. We shouldn't use to pursue the translations it because they are not tangent to the horizon. 298 00:49:36,780 --> 00:49:55,380 Maciej Kolanowski: So they are totally artificial from this point of view. So once asked about some natural is what kind of transform engagements permissions are natural from the point of horizon and require gauging variance with respect to them. 299 00:49:58,830 --> 00:50:14,040 Maciej Kolanowski: Okay, and then let us go to the last topic of today and namely this very basic observation that generators of the Citigroup dinner commute. 300 00:50:14,490 --> 00:50:34,440 Maciej Kolanowski: And so it follows the day charges are not very young and their, their actions. So if we have some solution if we transfer to linear is Einstein equations then. And if we translate this solution we obtain solution with different energy and we actually tracked 301 00:50:35,730 --> 00:50:36,900 Maciej Kolanowski: It is really the case. 302 00:50:39,510 --> 00:50:50,670 Maciej Kolanowski: So no natural question will be, whether this is a problem or not. We expected or not from a physical energy and 303 00:50:51,900 --> 00:51:06,270 Maciej Kolanowski: So geometrical meaning is quite clear, namely that this T vector would you defense energy is fixed fixed by a plus is. So roughly speaking, by this point where source hits cry. 304 00:51:07,350 --> 00:51:10,350 Maciej Kolanowski: And translations, not at this point. So, 305 00:51:12,780 --> 00:51:29,370 Maciej Kolanowski: And this is a geometrical meaning and. But the question still remains about physical meaning of this cutie. Especially if we had more sources or so on and then it's this i plus is not uniquely sound is not somehow uniquely defined 306 00:51:30,990 --> 00:51:39,000 Maciej Kolanowski: So, let us start with totally trivial situation that we have perturbation, on the whole, the sitter, which is topology. They are times as free 307 00:51:40,110 --> 00:51:58,560 Maciej Kolanowski: And we have perturbations, which are global defined without any singular just whatsoever. Then since we have a compact cushy surface all such perturbations ma muscle vanishing all the sitter charges. Oh, extremely few it should be data of view of God. 308 00:52:00,720 --> 00:52:14,370 Maciej Kolanowski: So it is not a surprise at all that it's true. So, so, so this is true because our both energy and momentum is zero, not very interesting either say 309 00:52:18,240 --> 00:52:31,980 Maciej Kolanowski: So now, from this we restrict ourselves to one Hubble or one carapace and we don't care about universe outside. So thanks to this, we can have some finite energy and financial momentum. 310 00:52:34,140 --> 00:52:34,920 Maciej Kolanowski: So the first 311 00:52:36,030 --> 00:52:47,550 Maciej Kolanowski: Simple scenario is such to do have some a God given waste which comes from the fraud. The cosmological horizon. They are not produced by any sort within our patch. 312 00:52:48,930 --> 00:52:57,000 Maciej Kolanowski: And they have some momentum say to the right. And then if we move this solution to the right is actually cool kind of look 313 00:52:58,050 --> 00:53:01,530 Maciej Kolanowski: Like we move them in time, not in 314 00:53:03,300 --> 00:53:15,600 Maciej Kolanowski: And not in space, but it simply means that it would means that the same solution entered expanding universe at a different point of time. 315 00:53:16,410 --> 00:53:34,200 Maciej Kolanowski: And but it is an expanding universe. So we don't expect that we've pockets entering a different times has have the same energy. Actually, I think it would be much weird. The other ones from this point of view, it's totally natural and there's no surprise here. 316 00:53:35,970 --> 00:53:39,900 Maciej Kolanowski: Then we have some astrophysical gravitational waves. 317 00:53:43,980 --> 00:53:47,520 Maciej Kolanowski: And and obviously our previous segments don't work. 318 00:53:50,010 --> 00:53:56,280 Maciej Kolanowski: Because now they were produced here at some the visit some physical moment. 319 00:53:57,540 --> 00:54:05,820 Maciej Kolanowski: However, the whole system's a binary black horse and repetition ways admitted her husband, she momentum. If 320 00:54:07,110 --> 00:54:32,820 Maciej Kolanowski: We are in their breasts time. And so the energy isn't very so we somehow rediscovered in this way this origin problem of Penrose that by this simple but by translating sources and also waves we mixed Columbia. Columbia, there are additive modes and also their energies. 321 00:54:34,080 --> 00:54:35,490 Maciej Kolanowski: So it would mean 322 00:54:36,810 --> 00:54:39,840 Maciej Kolanowski: So it would mean that we have 323 00:54:41,310 --> 00:54:42,780 Maciej Kolanowski: And that 324 00:54:43,920 --> 00:54:45,690 Maciej Kolanowski: This cutie is 325 00:54:46,710 --> 00:54:49,740 Maciej Kolanowski: It is somehow problematic in such a sense 326 00:54:51,060 --> 00:54:53,520 Maciej Kolanowski: That from the point of view of different origin. 327 00:54:54,570 --> 00:55:08,670 Maciej Kolanowski: It would be different. But what would be a invariant is combined energy of radiative and Columbia mode. And then in real astrophysical situations like Lego 328 00:55:09,750 --> 00:55:21,270 Maciej Kolanowski: It is actually not an energy that is measured, but much more observational so perhaps it is much we need to look into this more, but perhaps 329 00:55:22,350 --> 00:55:30,330 Maciej Kolanowski: Somehow, one, one, have no better way of fixing this origin by actually knowing when when and where this happened. 330 00:55:31,470 --> 00:55:33,660 Maciej Kolanowski: Okay, so let me conclude now. 331 00:55:35,100 --> 00:55:48,330 Maciej Kolanowski: And we have derived muscles formula scribe for the linear is gravity, we checked that it is the only gauging variant familiar with the proper lambda to zero limit. 332 00:55:51,540 --> 00:56:11,730 Maciej Kolanowski: We calculated the flux of energy for all the cosmological horizon and we tracked that it is it has correct lambda zero limit. And we also check, at least at leading all the, what is going on with fields defined nearby and in this limit. 333 00:56:14,130 --> 00:56:15,990 Maciej Kolanowski: And we and we discussed 334 00:56:17,010 --> 00:56:26,160 Maciej Kolanowski: What the what are consequences of the fact that moment and that translation and time translation in the City University not commute. 335 00:56:27,780 --> 00:56:29,490 Maciej Kolanowski: Okay, so thank you for your attention. 336 00:56:40,200 --> 00:56:41,130 Jorge Pullin: Any questions. 337 00:56:50,160 --> 00:56:54,750 Abhay Ashtekar: I have a couple of questions if there is nobody else. I mean, if somebody else has questions, please go ahead before me. 338 00:56:59,130 --> 00:57:01,320 Abhay Ashtekar: Yeah okay so 339 00:57:02,520 --> 00:57:04,680 Abhay Ashtekar: I took lessons. I mean, the 340 00:57:06,030 --> 00:57:13,860 Abhay Ashtekar: Oh, there's a there's a chatting somebody saying that. How about the question I asked or something like that. So do you want to answer that first 341 00:57:14,010 --> 00:57:21,210 Maciej Kolanowski: Yeah, yeah. Yes, of course. So hungry asked, it seems that you are using the definition of Hamiltonian proposed by Waltons lupus. 342 00:57:22,410 --> 00:57:31,440 Maciej Kolanowski: In 2000 in their construction is independent of the boundary. We also need to consider the integrated problem in the construction and 343 00:57:33,750 --> 00:57:34,860 Maciej Kolanowski: I'm sorry I'm not 344 00:57:36,270 --> 00:57:40,380 Maciej Kolanowski: So, so actually we we use 345 00:57:41,700 --> 00:57:55,230 Maciej Kolanowski: That there was a few works actually by word on this topic of Hamiltonian description and we actually used him a little bit newer one by one and how lots 346 00:57:58,470 --> 00:58:03,540 Maciej Kolanowski: And in which they actually don't care at all about integral billet at 347 00:58:04,800 --> 00:58:17,970 Maciej Kolanowski: At infinity, I guess, in contrast to this old proposal where where you had a few terms and you need. I think you needed to show that one of them is exit is the track. 348 00:58:21,000 --> 00:58:22,740 Maciej Kolanowski: They remember it correctly. 349 00:58:23,250 --> 00:58:24,030 Hongwei Tan: Or ish 350 00:58:26,730 --> 00:58:27,720 Hongwei Tan: I mean, the 351 00:58:28,920 --> 00:58:30,030 Hongwei Tan: Problem and 352 00:58:31,290 --> 00:58:31,560 Hongwei Tan: Who 353 00:58:33,480 --> 00:58:33,990 Hongwei Tan: Knew 354 00:58:35,850 --> 00:58:36,480 Hongwei Tan: And then 355 00:58:37,860 --> 00:58:38,550 Hongwei Tan: They can get 356 00:58:39,780 --> 00:58:40,830 Hongwei Tan: They can get there. 357 00:58:47,100 --> 00:58:48,030 Hongwei Tan: You go 358 00:58:52,140 --> 00:58:52,680 Hongwei Tan: Well, 359 00:58:57,300 --> 00:58:58,350 Hongwei Tan: The problem I mean 360 00:59:04,740 --> 00:59:10,530 Maciej Kolanowski: I'm sorry, I'm afraid I didn't exactly understand what you just said. 361 00:59:11,940 --> 00:59:14,310 Maciej Kolanowski: Perhaps you could repeat or right 362 00:59:18,270 --> 00:59:18,510 Okay. 363 00:59:30,030 --> 00:59:32,580 Jorge Pullin: So perhaps while he writes, you can address a base question. 364 00:59:33,060 --> 00:59:33,630 Yeah, sure. 365 01:00:13,380 --> 01:00:20,490 Abhay Ashtekar: Did you I, my question was is the first question is about the flux through the horizon and 366 01:00:20,520 --> 01:00:21,690 Abhay Ashtekar: Yes, it was whether 367 01:00:23,280 --> 01:00:29,130 Abhay Ashtekar: What you're talking about is on Page 24 the formula you give is that the final result or 368 01:00:41,580 --> 01:00:43,440 Maciej Kolanowski: This one, yeah. 369 01:00:43,500 --> 01:00:52,590 Abhay Ashtekar: Is that your dessert for the, I mean, is this supposed to be. I suppose this is supposed to the flux of the energy because you say to edge. Lots of 370 01:00:52,650 --> 01:00:56,160 Maciej Kolanowski: Energy after integrating after the integration of course 371 01:00:56,730 --> 01:01:00,690 Abhay Ashtekar: Of the integration or the final touch you will get this this answer or 372 01:01:01,110 --> 01:01:01,830 Abhay Ashtekar: You get 373 01:01:02,550 --> 01:01:07,290 Maciej Kolanowski: It at finite are it is a cosmological horizon. 374 01:01:07,380 --> 01:01:09,810 Abhay Ashtekar: Right, right. But in terms of the 375 01:01:11,040 --> 01:01:18,360 Abhay Ashtekar: It's still a finite no code that is going on. So you're looking at finite region of the of the cosmological horizon. Yeah. 376 01:01:19,650 --> 01:01:24,180 Maciej Kolanowski: Well, a priori. Yes, but we actually know that boundary terms are 377 01:01:24,180 --> 01:01:25,800 Maciej Kolanowski: Not correct if you look 378 01:01:25,830 --> 01:01:26,130 Maciej Kolanowski: On the 379 01:01:27,240 --> 01:01:27,870 Maciej Kolanowski: Interval 380 01:01:28,590 --> 01:01:37,680 Abhay Ashtekar: Ice. So therefore, for the boundary. So therefore, the statement is that you are looking at the flux through entire cosmological horizon. Is that correct, yes. 381 01:01:38,580 --> 01:01:55,230 Abhay Ashtekar: Okay, but then is this flux positive, we can just check looking at. I mean, we know it should be positive because the killing vector field is future directed. Now there. So, can you check. I mean, I can't tell. Look at our formula, whether it is manifesting positive definite or not. 382 01:01:59,760 --> 01:02:03,510 Maciej Kolanowski: Check it. But it's definitely a good security. 383 01:02:07,980 --> 01:02:08,970 Abhay Ashtekar: Sorry, I can't hear you. 384 01:02:12,840 --> 01:02:17,220 Maciej Kolanowski: We didn't do it, but it seems like a good security check 385 01:02:19,950 --> 01:02:20,640 Maciej Kolanowski: Can you hear me. 386 01:02:21,570 --> 01:02:33,120 Abhay Ashtekar: Yeah okay yeah I understand now. Okay. And then the first the question. The other question was about your first part, which had to do with scribe and you talk about the pseudo super translations. 387 01:02:33,660 --> 01:02:38,970 Abhay Ashtekar: Yeah, so, so they do include time translation. 388 01:02:39,570 --> 01:02:40,110 Maciej Kolanowski: Years of 389 01:02:40,440 --> 01:02:49,860 Abhay Ashtekar: Times. Okay, so what, why, at once they do say something like that. We know that this is gauge and therefore energy should not depend on them or something. 390 01:02:51,120 --> 01:02:51,480 Maciej Kolanowski: Well, 391 01:02:53,040 --> 01:02:54,780 Abhay Ashtekar: But I mean time constellation. 392 01:02:55,860 --> 01:02:58,500 Abhay Ashtekar: Is the generator of this right so it's not gauge 393 01:02:59,610 --> 01:03:02,250 Maciej Kolanowski: Yes, of course. So it is 394 01:03:04,320 --> 01:03:18,060 Maciej Kolanowski: It is this, those are awesome topic symmetries in such a sense that for Molly. They look like gauge like gauge transformations and bad such that 395 01:03:19,350 --> 01:03:21,000 Maciej Kolanowski: Do not vanish at infinity. 396 01:03:23,970 --> 01:03:30,990 Abhay Ashtekar: Yet what is confusing to me is really that. Do you have a natural affiliation of infinity of Scott 397 01:03:35,130 --> 01:03:45,450 Maciej Kolanowski: We what we work in linear gravity. So yes, Cry is has natural color is natural, our times. So 398 01:03:46,680 --> 01:03:58,890 Abhay Ashtekar: Then I agree, but it is it is that, but so you're using the foliage of sky, which is somehow given to you by the killing vector that you're using. Right. I'm not vertical line in the Penrose diner. Is that right, 399 01:03:59,670 --> 01:04:01,380 Maciej Kolanowski: Yeah, okay. 400 01:04:02,610 --> 01:04:06,960 Abhay Ashtekar: So so so you got this super translational super translations. 401 01:04:09,060 --> 01:04:12,150 Abhay Ashtekar: And I bet generators of 402 01:04:13,620 --> 01:04:15,480 Abhay Ashtekar: Audio have super moment today or what 403 01:04:17,370 --> 01:04:19,950 Maciej Kolanowski: Well, definitely, you could define them. 404 01:04:21,360 --> 01:04:36,180 Maciej Kolanowski: As they kind of tried to indicate, we don't know what's the status of those supersede the momentum and to whether they are associated with some sort of the gravitas, or what 405 01:04:37,740 --> 01:04:38,880 Abhay Ashtekar: But do you have a formula for that. 406 01:04:40,860 --> 01:04:42,030 Maciej Kolanowski: No, not yet. 407 01:04:42,810 --> 01:04:43,650 Abhay Ashtekar: Okay, thank you. 408 01:04:47,460 --> 01:04:49,200 Jorge Pullin: Judges there. Yeah. 409 01:04:49,740 --> 01:04:53,670 Maciej Kolanowski: So they have some boundary terms to consider the non integrated part in the proposal. 410 01:05:00,690 --> 01:05:01,440 Maciej Kolanowski: Oh, okay. 411 01:05:04,680 --> 01:05:11,550 Maciej Kolanowski: All right, so I what I mentioned was the different work, namely one by Walt and I are 412 01:05:13,350 --> 01:05:14,640 Maciej Kolanowski: And and 413 01:05:15,780 --> 01:05:34,410 Maciej Kolanowski: Okay, so okay so so knowing this, since we did not follow this proposal by Walt and Zoo pass and because we simply decided at the beginning that we don't know, and that we don't care. 414 01:05:35,670 --> 01:05:43,980 Maciej Kolanowski: That boundary boundary terms are problematic and to we want to look at them only at the very ending 415 01:05:45,480 --> 01:06:09,120 Maciej Kolanowski: At the very end it by some different arguments. And so we did not consider at this world and to pass a Newtonian then it although it is possible that it is the one who still at our US. And if it is, so then they unfortunately obtain some infinities 416 01:06:10,290 --> 01:06:11,910 Maciej Kolanowski: But I will need to check it. 417 01:06:18,690 --> 01:06:19,620 Jorge Pullin: Any other questions. 418 01:06:22,710 --> 01:06:36,150 Jorge Pullin: So I have one you started talking about, like, oh, so I guess what, what is your message to to, like, oh, I mean, it's sort of implicit in your equation 25 but this equation is kind of difficult to interpret. Like, I don't see what lambda is in it, for instance. 419 01:06:36,690 --> 01:06:39,180 Maciej Kolanowski: Yes. Okay, so lambda 420 01:06:48,000 --> 01:06:51,900 Maciej Kolanowski: Lambda is in this age zero. So, this is 421 01:06:52,890 --> 01:06:53,340 Jorge Pullin: So that's the 422 01:06:54,150 --> 01:06:54,720 Lambda 423 01:06:55,800 --> 01:06:58,680 Jorge Pullin: So that's the extra term with respect to this and politically flaccus 424 01:06:59,220 --> 01:07:00,870 Maciej Kolanowski: Yes, exactly. Okay. 425 01:07:06,270 --> 01:07:07,260 Jorge Pullin: Any other questions. 426 01:07:08,190 --> 01:07:23,010 Abhay Ashtekar: But I mean, it's definitely true that there is extra day. But on the other than the he is that he is writing down are also different right because of solutions to utilize the equations on the sitter background and not I'm in class case basis. So 427 01:07:23,130 --> 01:07:24,210 Abhay Ashtekar: Every he is different. 428 01:07:24,300 --> 01:07:25,680 Abhay Ashtekar: But in addition to that, there is that 429 01:07:26,730 --> 01:07:28,560 Abhay Ashtekar: There's an implicit lambda in every edge. 430 01:07:28,770 --> 01:07:29,280 Marriage. 431 01:07:30,390 --> 01:07:38,610 Maciej Kolanowski: But, in a sense, this equation 25. It is almost written in terms of initial data. 432 01:07:40,590 --> 01:07:42,600 Maciej Kolanowski: And so, in this sense. 433 01:07:43,770 --> 01:07:57,030 Maciej Kolanowski: You could start with the same initial data in Minka you could consider solutions which has the same behavior. Behavior at sky and the differences are only in the bulk 434 01:08:04,980 --> 01:08:11,520 Jerzy Lewandowski: Right, so you can consider age minus one to be independent of lambda and 435 01:08:17,910 --> 01:08:22,650 Jerzy Lewandowski: And and h zero, you would be proportional to lambda 436 01:08:24,090 --> 01:08:25,530 Abhay Ashtekar: Why, but on the other hand, if you just 437 01:08:26,100 --> 01:08:27,450 Jerzy Lewandowski: You would be also independent 438 01:08:28,830 --> 01:08:29,760 Abhay Ashtekar: But if you add some 439 01:08:30,060 --> 01:08:33,030 Abhay Ashtekar: Source inside on that vertical line that 440 01:08:34,200 --> 01:08:38,940 Abhay Ashtekar: That was drawn in the in the Penrose diagram. And if you calculate edge from that. 441 01:08:39,990 --> 01:08:49,980 Abhay Ashtekar: That is what logo, people are talking about writing to this much more sophisticated things, but for the quadruple formula. For example, the leading water current contribution. 442 01:08:51,930 --> 01:08:52,890 Abhay Ashtekar: That 443 01:08:54,750 --> 01:09:10,260 Abhay Ashtekar: They want to understand how does it relate to the sources not abstract edge. Right. So if you calculated coming from the sources, which is what they do, then he would depend on lambda. And there he does not depend on lambda 444 01:09:12,060 --> 01:09:18,870 Abhay Ashtekar: If you don't worry about property. The sources. Then I completely agree with what both of you are saying, but on the other hand, 445 01:09:20,040 --> 01:09:22,290 Abhay Ashtekar: I mean, that's not what local people interested in 446 01:09:23,280 --> 01:09:30,180 Maciej Kolanowski: Of course, rather. My point was that what is actually really measured is this part. 447 01:09:31,620 --> 01:09:32,940 Maciej Kolanowski: Oh, sorry. 448 01:09:34,320 --> 01:09:41,430 Maciej Kolanowski: What is actually measured is this part and and to not some bad behavior. 449 01:09:44,400 --> 01:09:46,140 Maciej Kolanowski: You only see leading 450 01:09:47,610 --> 01:09:56,940 Maciej Kolanowski: Lady, or at least I think so. Did legal you only see moving or the terms in one over our expansion in reality. 451 01:10:02,730 --> 01:10:10,410 Abhay Ashtekar: Yeah but Horace. I think we're going in circles. So I will say one more thing in this stuff Horace question was, what are we telling to the library people 452 01:10:11,070 --> 01:10:11,430 Maciej Kolanowski: Mm hmm. 453 01:10:11,580 --> 01:10:22,920 Abhay Ashtekar: And if we're going to tell something in live with people, then they are interested in not just looking at that age abstractly, but H which is produced by some sources like such as compact binaries. 454 01:10:24,270 --> 01:10:26,520 Abhay Ashtekar: And then to the approximation, you're working 455 01:10:28,080 --> 01:10:32,040 Abhay Ashtekar: The that he that you circled would also depend on 456 01:10:34,410 --> 01:10:41,250 Abhay Ashtekar: OOD also. Yeah, you said it also depends on this land up there right but they're also calculating the total energy 457 01:10:43,290 --> 01:11:01,800 Abhay Ashtekar: And that total energy. They're calculating would only also depend on exactly the the edge that you are circled whereas your total energy depends on other things as well. Yeah, so that so that so that is a different that we can tell to the, I mean, you will tell to the live of paper. Oh. 458 01:11:02,460 --> 01:11:05,070 Maciej Kolanowski: Yeah, thank you. It's very good point. 459 01:11:05,370 --> 01:11:07,020 Maciej Kolanowski: I think we could actually 460 01:11:07,230 --> 01:11:32,400 Maciej Kolanowski: Take your solutions to with surface those using and green functions and translate them to the Bondi frame to actually obtain flat mass loss formula and so obtain basically quadruple formula, but for financial times. I think this is was something one could do and to actually make contact. 461 01:11:33,000 --> 01:11:35,400 Maciej Kolanowski: With observations. Thank you. 462 01:11:40,050 --> 01:11:41,160 Jorge Pullin: Any other questions. 463 01:11:45,990 --> 01:11:47,130 Jorge Pullin: thank the speaker again.