MigL 1179 Posted June 22 (edited) I am aware that Einstein-Cartan torsion, to accommodate intrinsic angular momentum, the modified Dirac equation then implies fermions have 'spatial extension'. This means that BHs smaller than 10^16 kg are not possible, and the energy required to produce such a BH, is 39 orders of magnitude greater than available at the LHC ( see my post in this thread, on June 15, 1st page ). But Einstein-Cartan GR, while it seems to be the right path forward, does have some difficulties and is awaiting observational evidence, as opposed to 'regular' GR, sans torsion ( torsion 'walls' and rotating universe; Mordred may have more info regarding observations ) I'm also aware that electron degeneracy ( Pauli exclusion ) stops further collapse in a white dwarf star, and neutron degeneracy stops further collapse in a neutron star. But, what exactly, would be the mechanism in Einstein-Cartan GR that stops gravitational collapse of a BH to a singular point ? Just the fact that E-C GR doesn't support singularities, doesn't really clarify the matter Edited June 22 by MigL 0 Share this post Link to post Share on other sites

rjbeery 6 Posted June 22 On 6/19/2020 at 12:08 AM, Markus Hanke said: The existence of event horizons is trivially necessary, even in old Newtonian gravity without any GR effects. On 6/19/2020 at 12:08 AM, Markus Hanke said: This is mathematical fact, and not in dispute. Well if that's an argument then the singularity is necessary as well. 😜 On 6/19/2020 at 12:08 AM, Markus Hanke said: Sure, that is because coordinate time is what a distant observer records on his own clock. It is not what a clock located at the horizon itself will record. Time in GR is a purely local concept, so in order to examine the physics of this, you need to use a clock that is located at or at least near the horizon. The Schwarzschild coordinate chart does not cover the horizon nor the interior region, it covers only the exterior spacetime. There's no need to do this because my objection involving the event horizon using Schwarzschild coordinates only concerns the exterior region. All finite space and time have been accounted for. Every point (r=0, t<infinity) is represented, mathematically and physically, prior to the event horizon's creation. This has a literal, physical meaning. This mathematical fact does not vanish by changing coordinate charts or imparting angular momentum. 0 Share this post Link to post Share on other sites

md65536 340 Posted June 22 Earlier you wrote: On 6/17/2020 at 4:41 PM, rjbeery said: To see that this is a problem, consider the coordinate of the black hole completing its evaporation at t=100 in coordinate time. The point (r=0, t=100) is represented both at the event horizon formation and also after the black hole is gone. Can you remind us of the situation you're describing (I've lost track)? Whose coordinate time are you talking about here? It sounds elsewhere like you're talking about a Schwarzschild black hole, at rest (and evaporating) in the coordinates of an observer at infinity. However it also sounds like the Penrose diagram doesn't show those time coordinates, and the statement above doesn't match those coordinates either??? When you speak of time, if you could mention in each case whose coordinates you're referring to, that might make it clearer. 0 Share this post Link to post Share on other sites

rjbeery 6 Posted June 22 I'm referring to coordinate time (i.e. the infinite observer) when I make the statements below. 5 hours ago, rjbeery said: There's no need to do this because my objection involving the event horizon using Schwarzschild coordinates only concerns the exterior region. All finite space and time have been accounted for. Every point (r=0, t<infinity) is represented, mathematically and physically, prior to the event horizon's creation. This has a literal, physical meaning. This mathematical fact does not vanish by changing coordinate charts or imparting angular momentum. In my experience there can be a tendency in forums to obfuscate through complexity, or at least unintentionally over-complicate a problem. Looking at the Schwarzschild solution for a black hole of radius zero should make it obvious that any sort of evaporation leads to a contradiction. 0 Share this post Link to post Share on other sites

md65536 340 Posted June 22 (edited) 49 minutes ago, rjbeery said: I'm referring to coordinate time (i.e. the infinite observer) when I make the statements below. In my experience there can be a tendency in forums to obfuscate through complexity, or at least unintentionally over-complicate a problem. Looking at the Schwarzschild solution for a black hole of radius zero should make it obvious that any sort of evaporation leads to a contradiction. I'm not seeing any problem, except maybe mixing of different time coordinates. In my understanding, the point of having the observer at infinity is that it is "shielded" from any effects of spacetime curvature. In its coordinates, you could say eg. the black hole formed very far away and at coordinate time (ie. observer's local time) t=0, remained at rest, had a lifetime of 100 units of coordinate time, and finished evaporating at t=100, then sometime later at t>100 some other event happened at the location of the black hole. The same could be said if instead of a black hole, you're talking about a snowball with negligible mass. Neither has any effect on the coordinate time of the observer at infinity. There is nothing contradictory in the coordinate times of this observer on its own. So clearly we're comparing the times of different observers???, but it's not clear to me what other times you're speaking about here. Also, it should be possible to choose foliations of spacetime such that any events in the interior of the black hole are assigned meaningless coordinate times anywhere in [0, 100]. However, they would have no physical significance to the observer, and there'd be no way to break causality or create a contradiction through your choice. Edited June 22 by md65536 0 Share this post Link to post Share on other sites

Markus Hanke 323 Posted June 23 18 hours ago, rjbeery said: Well if that's an argument then the singularity is necessary as well. 😜 Yes, in classical and conventional GR the singularity is indeed unavoidable. But since the spacetime region containing the final stages of the collapse is outside the domain of applicability of GR, I do not consider this to be an issue. The appearance of a singularity simply means that the domain of applicability of GR is limited - just like is the case with any other model in physics. 18 hours ago, rjbeery said: There's no need to do this because my objection involving the event horizon using Schwarzschild coordinates only concerns the exterior region. All finite space and time have been accounted for. Every point (r=0, t<infinity) is represented, mathematically and physically, prior to the event horizon's creation. This has a literal, physical meaning. This mathematical fact does not vanish by changing coordinate charts or imparting angular momentum. Prior to the event horizon’s creation, there is no black hole, and you can use the maximally extended Schwarzschild solution to cover both the interior and exterior of the spherically symmetric mass. Once the collapse process passes a critical stage, the horizon appears at some finite distance, and the Schwarzschild metric no longer applies since the spacetime in question is now no longer Schwarzschild. 13 hours ago, rjbeery said: Looking at the Schwarzschild solution for a black hole of radius zero should make it obvious that any sort of evaporation leads to a contradiction. There is no contradiction, because once you have evaporation, the Spacetime is by definition not Schwarzschild. You can’t “look at the Schwarzschild solution” and talk about evaporation at the same time. This is what I have attempted to explain in my previous comments. 20 hours ago, MigL said: But Einstein-Cartan GR, while it seems to be the right path forward, does have some difficulties and is awaiting observational evidence, as opposed to 'regular' GR, sans torsion ( torsion 'walls' and rotating universe; Mordred may have more info regarding observations ) Yes indeed. At the same time though there is no evidence to definitively rule it out, so it is considered a viable candidate for further research and consideration. 20 hours ago, MigL said: But, what exactly, would be the mechanism in Einstein-Cartan GR that stops gravitational collapse of a BH to a singular point ? Because of the presence of torsion in the interior of the collapsing mass-energy distribution, the geometry of spacetime is different than it would be for the equivalent scenario under GR. Einstein-Cartan just simply does not lead to a run-away collapse resulting in a geodesically incomplete region; it leads to a situation where beyond some critical point the geometry of spacetime is such that - put simply and I’m sure not very correctly - in terms of time evolution, the radial coordinate r trades places with its inverse 1/r. This is analogous to how space and time in some sense trade places below the horizon of a Schwarzschild black hole. The collapsing matter thus rebounds and thus expands back out as it ages into the future, rather than ending up in a singularity. Due to extreme gravitational time dilation in that region, this process would take a very long time, exceeding the total lifetime of the universe by some orders of magnitude, which is why we don’t see this happening all around us. Also, there would be extreme tidal forces in that collapse region, tearing apart everything, so whatever comes back out would be little more than uniform radiation. Note that there are no stationary black holes in Einstein-Cartan gravity, it is always a time-dependent process. At least this is my understanding of the situation, I am not actually much of an expert on Einstein-Cartan gravity. 0 Share this post Link to post Share on other sites

Mordred 1370 Posted June 23 On the use of Einstein Cartan for a rotating universe. The observational evidence via CMB etc strongly rules out a rotating universe. I recall seeing a study that suggested the likelihood being 1 part in a billion if I recall correctly when I had last looked into it. The metric though is still handy as it has all the metrics needed to model spacetime rotation. 0 Share this post Link to post Share on other sites

MigL 1179 Posted June 23 Leaving the Big Bang singularity aside, and considering Black Holes for the moment. Wiki has this to say about Einstein-Cartan geometries "According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular black hole. In the Einstein–Cartan theory, instead, the collapse reaches a bounce and forms a regular Einstein–Rosen bridge (wormhole) to a new, growing universe on the other side of the event horizon." From https://en.wikipedia.org/wiki/Einstein–Cartan_theory I have always thought universes growing out of a wormhole, or white hole, did not fit observational evidence. X-posted with Mordred 0 Share this post Link to post Share on other sites

rjbeery 6 Posted June 23 7 hours ago, Markus Hanke said: The collapsing matter thus rebounds and thus expands back out as it ages into the future, rather than ending up in a singularity. Due to extreme gravitational time dilation in that region, this process would take a very long time, exceeding the total lifetime of the universe by some orders of magnitude, which is why we don’t see this happening all around us. 6 hours ago, MigL said: I have always thought universes growing out of a wormhole, or white hole, did not fit observational evidence. This is why I put the emphasis on micro black holes -- GR predicts them, yet the fact that we can't detect them implies (almost demands) that evaporation of some sort occurs. That this evaporation must occur prior to the event horizon existing, on logical grounds, is what I've been unable to convey in this thread. 0 Share this post Link to post Share on other sites

Strange 4227 Posted June 23 2 hours ago, rjbeery said: This is why I put the emphasis on micro black holes -- GR predicts them GR allows them (big difference). I am not aware of any plausible mechanism for creating them nor any evidence that they exist. 2 hours ago, rjbeery said: yet the fact that we can't detect them implies (almost demands) that evaporation of some sort occurs. Or that they never existed in the first place. 2 hours ago, rjbeery said: That this evaporation must occur prior to the event horizon existing, on logical grounds, is what I've been unable to convey in this thread. Probably because you are wrong 0 Share this post Link to post Share on other sites

rjbeery 6 Posted June 24 4 hours ago, Strange said: GR allows them (big difference). I am not aware of any plausible mechanism for creating them nor any evidence that they exist. That's a distinction without a difference, and you have your logic backwards -- cosmic rays have no known nor plausible mechanism that might limit their incoming velocity as they enter our atmosphere. The energy required for a cosmic ray to collapse into a black hole isn't ungodly (due to their radius). To acknowledge cosmic rays but deny micro black holes is tantamount to declaring GR wrong. 4 hours ago, Strange said: Probably because you are wrong Possible, but I'm not here to convince others; I'm here to listen to and analyze objections. 0 Share this post Link to post Share on other sites

MigL 1179 Posted June 24 4 hours ago, Strange said: GR allows them (big difference). One that rjbeery doesn't seem to understand. GR allows for … white holes singularities naked singularities CTL and time travel wormholes and my mind is working only in one direction; I can't think of any more right now. Everyone else is free to contribute to the list of non-physical effects allowed by GR. ( maybe rjbeery will finally realize the difference ) 0 Share this post Link to post Share on other sites

Mordred 1370 Posted June 24 43 minutes ago, rjbeery said: That's a distinction without a difference, and you have your logic backwards -- cosmic rays have no known nor plausible mechanism that might limit their incoming velocity as they enter our atmosphere. The energy required for a cosmic ray to collapse into a black hole isn't ungodly (due to their radius). To acknowledge cosmic rays but deny micro black holes is tantamount to declaring GR wrong. The speed limit c applies to cosmic rays and quite frankly the mechanism that determines the velocity is understood. Secondly cosmic rays are produced by any star. You don't need micro blackholes. So that is a false assumption. 0 Share this post Link to post Share on other sites

Markus Hanke 323 Posted June 24 4 hours ago, rjbeery said: Possible, but I'm not here to convince others; I'm here to listen to and analyze objections. To be honest, this isn't how it comes across. You seem to pretty much ignore most of what is said to you, so I don't know what the purpose of this thread is actually supposed to be. 0 Share this post Link to post Share on other sites

rjbeery 6 Posted June 24 17 hours ago, MigL said: GR allows for … white holes singularities naked singularities CTL and time travel wormholes Of course, and if the physical conditions were right then those things may come to be...or not. But the physical conditions for micro black holes are likely met continuously in our atmosphere. 16 hours ago, Mordred said: The speed limit c applies to cosmic rays and quite frankly the mechanism that determines the velocity is understood. Secondly cosmic rays are produced by any star. You don't need micro blackholes. So that is a false assumption. Obviously c applies to cosmic rays - when I said "no known mechanism might limit their incoming velocity" I meant limit it as a percentage of c such that they would be prevented from having sufficient energy to predict a micro black hole. Your second comment is baffling. Which assumption is false? Micro black holes do not produce cosmic rays -- they are produced by them. 13 hours ago, Markus Hanke said: To be honest, this isn't how it comes across. You seem to pretty much ignore most of what is said to you, so I don't know what the purpose of this thread is actually supposed to be. If you could summarize MY position on this, how would you do so? 0 Share this post Link to post Share on other sites

MigL 1179 Posted June 24 5 hours ago, rjbeery said: Micro black holes do not produce cosmic rays -- they are produced by them. Really ? Cosmic rays enter the atmosphere billions of times, yet not a single micro BH has ever been detected. Maybe you can produce a citation of a detected micro BH. I can certainly post numerous citations of cosmic ray detections. 2 Share this post Link to post Share on other sites

Mordred 1370 Posted June 25 29 minutes ago, MigL said: Really ? Cosmic rays enter the atmosphere billions of times, yet not a single micro BH has ever been detected. Maybe you can produce a citation of a detected micro BH. I can certainly post numerous citations of cosmic ray detections. This post says it all +1 0 Share this post Link to post Share on other sites

md65536 340 Posted June 25 5 hours ago, rjbeery said: If you could summarize MY position on this, how would you do so? This is what I got from your posts: 1) A black hole and all the events in its interior can be described in the coordinates of an observer at infinity. 2) A Penrose diagram of an evaporating black hole shows that the formation and disappearance of a black hole have the same time coordinate. 3) If an event A has a coordinate time that is less than the coordinate time of an event B, then A happened before B (maybe even in B's past?). Problems with this: (1) The interior events do not have meaningful time coordinates for this observer. (2) If that's what the diagram really shows, then the coordinates used in that diagram can't be the same as for the observer in (1). (3) You're comparing coordinate times of events that have no causal connections, and their ordering is irrelevant, but you see "logic problems" by treating it as something physical. 2 Share this post Link to post Share on other sites

Markus Hanke 323 Posted June 25 (edited) 17 hours ago, rjbeery said: If you could summarize MY position on this, how would you do so? That is a really good question, because I still don't know what your position actually is. You seem to be saying that the concept of an evaporating Schwarzschild black hole is self-contradictory - which is trivially true, because Schwarzschild black holes are of course stationary by definition. But evaporating black holes aren't of the Schwarzschild kind, so where exactly is the issue? Then so you also seem to be saying that even ordinary Schwarzschild black holes are self-contradictory, because somehow event horizons can't exist? But I don't understand why you think this, because the reasons you give don't make any sense. Edited June 25 by Markus Hanke 2 Share this post Link to post Share on other sites

joigus 127 Posted June 25 17 hours ago, rjbeery said: If you could summarize MY position on this, how would you do so? Maybe it's something to do with this: -------------------------------------------- "The most misleading assumptions are the ones you don’t even know you’re making." Douglas Noel Adams Last Chance to See (1990) --------------------------------------------- A round of rep points for @MigL, @md65536, and @Markus Hanke for clarifying many aspects of the OP and the follow-ups. 0 Share this post Link to post Share on other sites

rjbeery 6 Posted June 27 On 6/24/2020 at 6:45 PM, MigL said: Really ? Cosmic rays enter the atmosphere billions of times, yet not a single micro BH has ever been detected. Agreed, which means that either 1) General Relativity is wrong, 2) some mysterious delimiter on the velocity of cosmic rays prevents them from reaching the critical energy required for a predicted micro black hole, or 3) the micro black holes evaporate before they can be detected. I'm working under the presumption of #3, and I feel it's fair to say that this is the same position held by most of the physics community today (as evidenced by the paper I linked to regarding the Large Hadron Safety Assessment Group). On 6/24/2020 at 8:11 PM, md65536 said: This is what I got from your posts: 1) A black hole and all the events in its interior can be described in the coordinates of an observer at infinity. 2) A Penrose diagram of an evaporating black hole shows that the formation and disappearance of a black hole have the same time coordinate. 3) If an event A has a coordinate time that is less than the coordinate time of an event B, then A happened before B (maybe even in B's past?). This is close, but regarding #1 -- the interior of a black hole cannot be described by the remote observer, and does not need to be. The infinite future is represented for a coordinate time observer B before mass crosses the event horizon. We have to take this literally. Pick a method of determining simultaneity, and then map those events of object A approaching the event horizon to the remote observer B; there will be events A that match to events B for any and all times/events for B from "now" until "eternity". Now, let the black hole evaporate, such that the black hole and A are simply gone and replaced by a new observer, C. Now, B and C can match events using our method of simultaneity, forever. In other words, If B were to describe what was happening in the region of the black hole at some certain time, he would claim that both A is asymptotically approaching it, and C is calmly residing there with no black hole in sight. Quote With the back-reaction of Hawking radiation taken into consideration, the work of Kawai, Matsuo and Yokokura [1] has shown that, under a few assumptions, the collapse of matter does not lead to event horizon nor apparent horizon. In this paper, we relax their assumptions and elaborate on the space-time geometry of a generic collapsing body with spherical symmetry. The geometry outside the collapsing sphere is found to be approximated by the geometry outside the white-hole horizon, hence the collapsing matter remains outside the Schwarzschild radius. As particles in Hawking radiation are created in the vicinity of the collapsing matter, the information loss paradox is alleviated. Assuming that the collapsing body evaporates within finite time, there is no event horizon. I found this paper today, and, based on the abstract, it's making a similar argument: Quote When Hawking radiation is turned on, it is assumed in the conventional model of a black hole [6] that the (apparent) horizon appears in finite time for a distant observer, although it is unclear how Hawking radiation can speed up the formation of horizon. (This is another way to see that a negative energy flux is needed in the conventional model.) Conventionally, it is also believed to be a good approximation to ignore Hawking radiation during the formation of a black hole, and consider Hawking radiation only after the horizon appears. By patching the Penrose diagram of black-hole formation in the absence of Hawking radiation with that of black-hole evaporation, one finds the Penrose diagram in Fig. 1 [6], which represents the conventional model of a black hole. Parse this paragraph carefully. It says that it's assumed that an event horizon can form with Hawking radiation...but we have no model for it. Therefore we "turn off" Hawking radiation to allow the event horizon to form, and then "turn it on" to produce the graph that I used to show that a contradiction resides in this logic. 0 Share this post Link to post Share on other sites

MigL 1179 Posted June 27 18 minutes ago, rjbeery said: Agreed, which means that either 1) General Relativity is wrong, 2) some mysterious delimiter on the velocity of cosmic rays prevents them from reaching the critical energy required for a predicted micro black hole, or 3) the micro black holes evaporate before they can be detected. Or maybe, because of torsion, micro BHs cannot form at those energies ( if at all ), even if cosmic ray energies are much higher than is available at the LHC. Who exactly predicted these micro BHs ????? 0 Share this post Link to post Share on other sites

md65536 340 Posted June 28 (edited) 2 hours ago, rjbeery said: Parse this paragraph carefully. It says that it's assumed that an event horizon can form with Hawking radiation...but we have no model for it. Therefore we "turn off" Hawking radiation to allow the event horizon to form, and then "turn it on" to produce the graph that I used to show that a contradiction resides in this logic. That paragraph is talking about the apparent horizon, and you're talking about the event horizon. See https://en.wikipedia.org/wiki/Apparent_horizon : Quote In the simple picture of stellar collapse leading to formation of a black hole, an event horizon forms before an apparent horizon.^{[2]} As the black hole settles down, the two horizons approach each other, and asymptotically become the same surface. If the AH exists, it is necessarily inside of the EH. Apparent horizons depend on the "slicing" of a spacetime. That is, the location and even existence of an apparent horizon depends on the way spacetime is divided into space and time. For example, it is possible to slice the Schwarzschild geometry in such a way that there is no apparent horizon, ever, despite the fact that there is certainly an event horizon.^{[3]} I don't know enough to see any problems here. We *need* to make assumptions to model the interior of a black hole (inside the event horizon) because we can't make any observations to test our models. But that's exactly why there are no real problems; if you say some model or assumption "logically" implies some physical phenomena or paradox, but it has no observable consequences, how can you claim it's a real problem? It's like the movie Interstellar, which made up a paradoxical imagination of the interior of a black hole. Yet Kip Thorne says something like that the movie doesn't break any scientific laws, but that's because there are no laws that say what is observed inside a black hole. The event horizon and evaporation are things that have physical significance outside of the black hole, including effects that can be observed. The apparent horizon can't be observed from outside. 2 hours ago, rjbeery said: This is close, but regarding #1 -- the interior of a black hole cannot be described by the remote observer, and does not need to be. The infinite future is represented for a coordinate time observer B before mass crosses the event horizon. We have to take this literally. Pick a method of determining simultaneity, and then map those events of object A approaching the event horizon to the remote observer B; there will be events A that match to events B for any and all times/events for B from "now" until "eternity". Now, let the black hole evaporate, such that the black hole and A are simply gone and replaced by a new observer, C. Now, B and C can match events using our method of simultaneity, forever. In other words, If B were to describe what was happening in the region of the black hole at some certain time, he would claim that both A is asymptotically approaching it, and C is calmly residing there with no black hole in sight. Oh, I see a little clearer the problem that you're describing. But it's easily resolved. As Markus pointed out, a Schwarzschild BH doesn't evaporate. An infalling object A gets stuck on the event horizon "forever" (in B's coordinates), but the event horizon continues to exist forever. If on the other hand the BH evaporates in finite time, the event horizon no longer exists when the BH has evaporated away. Observer B doesn't have events occurring at the event horizon at times when the event horizon doesn't exist. Either A falls in and the black hole evaporates and A's world line ends with a finite coordinate time (in B's coords), or the black hole doesn't evaporate and the event horizon lasts forever with A on it (in B's coords), but not both. If you describe A and B in terms of causal connections, or events involving the other that they can observe, they're going to agree, no matter what realistic thing you have them do. In terms of simultaneity alone, they don't need to agree, and there's nothing paradoxical about that. But yes, object A can't both be trapped on a static event horizon forever, and let the event horizon evaporate in finite time. The event horizon can't be both static and non-static in a given reference frame. Edited June 28 by md65536 0 Share this post Link to post Share on other sites

Markus Hanke 323 Posted June 28 5 hours ago, rjbeery said: We have to take this literally. No, we have to take this locally. It’s Schwarzschild coordinate time, so this is what a far-away stationary clock measures locally in its own frame of reference. It is not what physically happens anywhere else. In GR, time is always a purely local concept. 5 hours ago, rjbeery said: Pick a method of determining simultaneity, and then map those events of object A approaching the event horizon to the remote observer B; Again, this is not possible. Time is a purely local concept in GR; there is, in general, no notion of simultaneity across extended regions of curved spacetime, and you can’t map notions of space and time local to some far-away observer into anything that happens anywhere else. In particular not to test particles in free fall, which aren’t stationary. You can define static hypersurfaces of simultaneity based on the coordinate system you have chosen (in Schwarzschild, these will be nested spheres), but that is not the same thing. 5 hours ago, rjbeery said: Parse this paragraph carefully. It talks about the conventional model for this - that means you use Schwarzschild spacetime, allow the mass terms to vary, and see what happens. This is meant as an approximation and a teaching tool, because the maths are easy to do on paper, unlike is the case for a full description. But as I have attempted to point out several times now, in actual fact any kind of black hole that isn’t stationary can’t physically be Schwarzschild, so it is little surprise that the conventional model does not actually work too well. That was kind of the point of Hawking’s original paper (I recommend you read it) - he started with a conventional Schwarzschild black hole, and examined if and how it is compatible with quantum field theory; and unsurprisingly he found that it isn’t, so Schwarzschild black holes cannot actually occur in nature. At the very least, they have to be generalised to their radiating counterparts, the aforementioned Vaidya black holes. 6 hours ago, rjbeery said: but we have no model for it Yes we do. We can use quantum field theory in conjunction with the Vaidya solution to model Hawking radiation in a non-stationary spacetime. This has been done by several authors, e.g. here. However, the result of this is a geometry that is vastly more complex than Schwarzschild, and contains several different types of surfaces - event horizons, apparent horizons, Killing horizons, and trapped surfaces. In particular, in can be explicitly shown that a far-away observer will receive information about the black hole’s state in finite coordinate time, unlike would be the case in Schwarzschild. 0 Share this post Link to post Share on other sites

Halc 5 Posted June 28 10 hours ago, Markus Hanke said: Time is a purely local concept in GR; there is, in general, no notion of simultaneity across extended regions of curved spacetime, and you can’t map notions of space and time local to some far-away observer into anything that happens anywhere else. ... You can define static hypersurfaces of simultaneity based on the coordinate system you have chosen (in Schwarzschild, these will be nested spheres), but that is not the same thing. It seems that there is no coordinate system that foliates all of spacetime. This seems to be an interesting argument against any philosophy of time that posits an absolute coordinate system (a preferred frame of one sort or another). Presentism is only a subset of these philosophies. The inability to identify any coordinate system that can consistently map any pair of events as to which occurs first seems to me to be a fatal flaw in such a philosophy. 0 Share this post Link to post Share on other sites