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How do black holes grow? 
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#19
Nov1812, 02:13 AM

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For our purposes here, the key point is that this model predicts that the spacetime *does* contain an event horizon and a black hole region. What happens is that the outer surface of the collapsing matter, as it gets smaller and the matter gets denser, eventually becomes a "trapped surface" (this is a modern term and was not used in the original OppenheimerSnyder paper); that is, it is a surface from which even outgoing light (light emitted directly radially outward) does not move outward (that is, it doesn't move to a larger radius). Once this happens, the collapsing matter is doomed to continue collapsing all the way to infinite density and infinite spacetime curvature at r = 0, leaving behind an event horizon and a black hole region inside the horizon. (Actually, the original OppenheimerSnyder paper, I believe, did not carry the analysis beyond the instant when the trapped surface forms; in other words, their original analysis was incomplete. But later work has confirmed their analysis and carried it to completion; the result is what I described above.) 


#20
Nov1812, 02:18 AM

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(Or perhaps the problem is the phrase "from an external observer's point of view". The computation I describe shows that no light signal from at or inside the horizon will ever reach the external observer; equivalently, it shows that the region of spacetime in which the external observer's time coordinate is finite does not contain the event horizon or the black hole. If this means the EH doesn't form "from the external observer's point of view", then that's fine, but you have to be very careful not to extend that claim into "the EH doesn't form, period", which is false; the spacetime *does* contain an event horizon and a black hole, and additional matter *can* fall through the horizon and into the black hole. So adopting the "external observer's point of view" forces you to walk a very fine line, to avoid claiming too much. In my experience, most people are not able to walk that line, so it's better, IMO, to just say flat out that the event horizon and the black hole *do* form, and that the "external observer's point of view" is the wrong one to use. But your mileage may vary.) 


#21
Nov1812, 02:33 AM

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"The observer outside always 'sees' a very near black hole, with an 'almost horizon' (note, this 'almost horizon' is blacker than anything else in the universe in finite time for the external observer  however, technically, it has not quite become a horizon as seen by the outside observer. When more matter falls in, the outside obsever sees the 'almost horizon' grow. So everything is always an 'almost black hole' as seen by an outside observer." What is observed in this case, and in the case of a fully formed black hole, is a region "blacker than anything else in the universe". But perhaps I should not have used that ECO term, because it has been used elsewhere in other contexts. You also said "Another way of putting it: claiming that the event horizon never forms because "it takes an infinite time as far as a distant external observer is concerned" is equivalent to claiming that the region of spacetime in which the distant observer's time coordinate is finite is the entire spacetime. This claim is false. ". I understood this to be the conclusion of the OppenherimerSnyder calculations. Where do they allow for any distant observer actually seeing a black hole form in a finite time? OK, I accept that their ideal observer is stationary relative to the forming BH, and an infinite distance fom any spacedistorting mass, but I don't believe these conditions affect the conclusion. There are other observers who see the black hole form, but they are local to it, and not distant. So I am not making a claim about all spacetime. And I'm not including spacetime inside a black hole, because that gets too complicated. Mike 


#22
Nov1812, 10:33 PM

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However, as soon as we talk about 'time at a distance' there is great ambiguity. This is not physically measurable. There are perfectly reasonable definitions (and that is all their can be  definitions) of 'time at a distance' such that a distant observer computes that collapse has occurred in finite 'time at a distance' and further infallers reach the singularity in finite 'time at a distance'. Note that SC coordinate time is a peculiar definition of time for distant observer in the following sense (in classical GR):  there events I cause, and observers receiving signals from me that are declared never to be simultaneous with any event on my future world line, even carried to infinity. If you simply modify SC simultaneity to include events caused by an external observer, then you attach finite times to event crossing and arrival at singularity. 


#23
Nov1812, 10:52 PM

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Let me make concrete a different definition for times assigned to distant events for distant observer of a collapse leading to spherically symmetric BH. This definition will match SC time for an observer at infinity for events 'near the observer', but will differ more and more for other events. [edit: removed statement about observer not 'near infinity', that is not quite true].
We posit the world line of some static, distant obsever (reference observer). For any event E, we find the event on this observer's world line such that light will reach the chosen event (call clock time for the reference observer for this emission event T0). The chosen event E has some SC r coordinate (r1). The reference world line has some other r coordinate(r0, always). We assign to E a T coordinate of: T0 + (r1r0)/c. The defines a perfectly plausible alternate time coordinate for the static observer at r0. It can be combined with SC r, theta and phi coordinates. With this modification to SC time, it is now true that r0 observer computes finite times for infall event horizon crossings, and infall times of reaching singularity. 


#24
Nov1812, 11:12 PM

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#25
Nov1912, 12:30 AM

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I have been trying to follow the discussions above and make some sense.
It appears to me now there is some disagreement between interpretations of GR on this point, with three possibilities supported by different scientists, i.e. black holes/event horizons:



#26
Nov1912, 12:58 AM

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 An observer riding with collapsing matter or falling in later will cross an EH and reach the singularity in finite time on their watch.  An observer remaining outside will never see an EH form, nor will they see any later infaller cross an EH (because it won't be seen to form). They will detect (gravitationally) increase in mass of 'black body' as new matter falls in, but no outside measurement will detect any information that an EH has actually formed. However, the delta between this observed almost BH and an eternal BH with actual event horizon, will grow smaller exponentially to the point where no conceivable measurement can distinguish. As soon as you go from what observers measure to what they might consider to be true based on computation you can make the following statements:  that the universe contains a BH according to theory (classical GR), is something any observer may compute. They all get the same result that the universe does contain such a thing (given the appropriate collapse).  There is no objective meaning to 'time at a distance' for events not observed. There is no objective meaning to 'what is over there now'. Depending on different plausible choice for this, you can say a distant observer considers an EH never to form, or to form at some well defined finite time. In either case, it is true that (per computation), the universe as a whole contains a BH with EH. 


#27
Nov1912, 02:15 AM

P: 181

The only beef I have about this (not with you, but with GR), is that a 'riding' observer happens to experience an 'event' that an external observer cannot accept will ever happen, no matter how long he waits for it. Also, he can only conclude that the Universe may contain objects very close to being black holes, but does not contain actual black holes, unless they were formed along with the Big Bang. 


#28
Nov1912, 04:25 AM

P: 3,187

 http://www.physicsforums.com/showthread.php?p=4129133 and from here:  http://www.physicsforums.com/showthread.php?p=4163727 and from here:  www.physicsforums.com/showthread.php?p=4164194 (and also a little in here:  www.physicsforums.com/showthread.php?t=647627) Thus it's a matter of interpretation of models, and the interpretation that you are looking for apparently began with Einstein's 1939 paper. In that interpretation a falling observer will not experience a falling through the horizon ("The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality"). For me that topic has been sufficiently discussed now, and it's sufficiently clear, so I'll leave it up to you in your thread. PS: I see your last remark in post #27. Just like me, your beef is not with GR but with an interpretation of GR. That is a big difference. 


#29
Nov1912, 09:17 AM

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#30
Nov1912, 09:27 AM

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Further, independent of observations, computationally there are many ways to relate distant events in the universe as happening at your 'now'. Both GR and SR say this is a matter of convention not physics. There are numerous simultaneity conventions a distant observer may choose such that they compute an EH and singularity have formed [I gave a simple, physical, definition of one in my post #23]. This in no way contradicts that they also compute they will never detect any information from these events. 


#31
Nov1912, 09:52 AM

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Consider an infinite number of observers, all simultaneously starting at the same point outside the BH, but undergoing different proper accelerations ranging from a=0 (free fall into the BH) to a=a_hover (allows keeping r=const). How would the free falling one be observed by the others? Which ones would see him cross the EH and after which time on their clocks? 


#32
Nov1912, 10:05 AM

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The behavior is very similar to a uniformly accelerating rocket and its Rindler horizon. If the rocket drops a series of probes, it will see them freeze, one after the other at its Rindler horizon (this is all SR). Only if it stops accelerating, so that the Rindler horizon overtakes it, will it see these dropped probes crossing the horizon, and see their subsequent history. 


#33
Nov1912, 02:54 PM

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Anyone moving radially with insufficient constant proper acceleration to hover will fall through the horizon in finite proper time (at which moment they'll see falling through anyone else who fell through before them). 


#34
Nov1912, 03:34 PM

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Consider the following example from special relativity. A ("Born rigid") rocket has constant proper acceleration in empty space, far from any gravity. At any instant in time, you can define distance and simultaneity according to an inertial observer who is momentarily at rest relative to the rocket. You can "glue" all these observers together to form a valid coordinate system ("Rindler coordinates") for the rocket. Here's a spacetime diagram showing the distance X and time T of an inertial frame, and the pink grid lines show the rocket's Rindler coordinates x and t. The curved line x=1 represents one point on the rocket. Dr Greg, Wikimedia Commons, CC BYSA 3.0 The white area above this chart is not covered by the pink grid. Even after waiting an infinite time t, none of the events in that area become simultaneous with an event on the rocket as measured by the rocket. Yet these events do have a finite inertial T coordinate. Would you say that the events in those areas "do not exist"? 


#35
Nov1912, 09:51 PM

P: 181

I feel the event I am talking about (matter crossing EH) is always in the future, getting asymptotically closer to the EH, but never reaching it. Yes, by our own clock, and my question is based on our own clock (can black hole EH grow for external observers?). I understand that the event may actually happen for an observer falling into the black hole, but by our clock, this falling observer also never reaches the event horizon! So I stand by the statement that the event "does not exist" or come to pass ever, by our clock. This is where I see a conflict. From our point of view, drawing a geometric parallel, two lines are asymptotic and only meet at infinity, and never cross over. For the observer falling into the BH, not only do the two lines meet, but they even cross over. I am getting the feeling that there is still some lack of appropriate interpretation of GR in this area, or perhaps, GR may have to be further generalized in this area for a proper interpretation of Universal events (If we accept the astronomical conclusion that black holes exist, and grow in finite time of external observers' clocks). That is, unless we accept the other possible explanation that black holes never really fully form, but get aymptotically closer to forming all the time. 


#36
Nov1912, 10:31 PM

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This is *not* true for the worldlines of two infalling objects that meet inside the horizon. "Length" along worldlines in spacetime means proper time, and the two objects will meet in a *finite* amount of proper time. You already agree with this, but you apparently haven't fully comprehended what it means. It means that the two lines are *not* "infinitely long" before they meet below the horizon, in the way that parallel lines on a Euclidean plane are "infinitely long" before they meet. You can only extend the two worldlines for a finite length before they meet, even though doing so covers an infinite range of the distant observer's time coordinate. In other words, when you have extended the two lines "to infinity" according to your clock, you have only extended them to a finite length in geometrically invariant terms. You have chosen a time coordinate that is so distorted at the horizon that it extends finite lengths (i.e., finite proper times) so they look like infinite lines. The analogy you are trying to draw with "infinite lines" in ordinary plane geometry does not work; the lines that "look infinite" to the distant observer because of his choice of time coordinate are *not infinite*. 


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