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OppenheimerSnyder model of star collapse 
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#73
Nov1812, 01:08 PM

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#74
Nov1812, 01:16 PM

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Note, we can readily do this between an infalling clock and a distant clock such that 3 pm on both clocks corresponds to the infalling clock a microsecond before hitting the singularity. Each clock would read its own proper time, and the relation between their world lines would be based on GP time coordinate instead of SC time coordinate (the time coordinate just being used to establish simultaneity relations). 


#75
Nov1812, 01:18 PM

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#76
Nov1812, 01:31 PM

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 starting from established classical results, wondering if one way causality and behavior of SC coordinate time may provide a hint at quantum treatment,  we then treat the the collapse quantum mechanically (using SC coordinates) and find that evaporation beats collapse. Therefore the information paradox never arises. And backfitting this result, we may choose to ignore anything classical GR says about the horizon and interior. And counter arguing papers are all on the second bullet above: you don't escape the information paradox that easily. Evaporation does not beat collapse. A deeper solution to the information paradox is needed. 


#77
Nov1812, 03:18 PM

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But since the blue region is above the horizon line (the 45 degree line going up and to the right), light signals from the black hole region can never get out to the gray region, which is the region covered by the distant observer's time coordinate. That's why the black hole region is not "visible" to the distant observer; he can never see light signals from it. But the region is there. 


#78
Nov1812, 03:20 PM

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#79
Nov1812, 08:21 PM

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"In Sec. III we verify the standard result that the formation of an event horizon takes an infinite (Schwarzschild) time if we consider classical collapse. This is not surprising and is often viewed as a limitation of the Schwarzschild coordinate system. To see if this result changes when quantum effects are taken into account.." Let me emphasize:  verify standard results  infinite Schwarzschild time No where are they claiming a new classical result; no where do they dispute (nor mention) the classical result that the in other coordinates the EH happens in finite coordinate time, and that the dust cloud crosses the EH in finite time for a clock following just above its surface. These are not concerns of the paper. The paper is clearly concerned with quantum corrections, wherein (if they are right) these other features go away. They believe in coordinate invariance, so the implication is that if quantum analysis says the collapsed object evaporates before the EH is formed in SC coordinates, then this means, in any coordinates, and for any observer, there is no EH at all. This is the new and fairly radical claim  all based on quantum corrections. If piece of matter transforms to radiation before a horizon is formed in coordinate system, the fact must be true in all. This is the controversial aspect of their work. [Edit: in reference to Dr. Greg's beautiful illustration in #64, the key point of the Krauss,et.al. paper is to argue that [due to quantum behavior  evaporation], the grey line curves up asymptotically to the top 45 degree line of the pink region, never entering the blue region. This means the blue region is not part of the solution at all. This is all coordinate independent geometry. The claim is not about interpreting something like classical OS spacetime; it is that, when quantum effects are considered, classical OS spacetime does not occur. What does occur looks very much like it, for a distant observer, for a very long time, but eventually, it can be distinguished  via the radiation  that the actual spacetime was never similar to an OS spacetime, in that the blue region never existed  at all, for any observer. If we translate the Krauss et. all. proposal to the experience of an observer on the collapsing shell, we get, instead of:  reaching a horizon, then a singularity, in finite clock time (for that observer) we get:  being converted to not quite thermal radiation, in finite clock time, without ever reaching the critical radius. If their result holds, and also applies to dust ball collapse, as they hope it does, then an interior observer of such a collapse would experience:  in finite time, evaporating to non quite thermal radiation before reaching a minimum radius. ] 


#80
Nov1812, 09:36 PM

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As I read it, the model in the Krauss paper is somewhat different from the "OS" model (by which I mean the modern version, not necessarily the version in the OS paper). The Krauss paper models a collapsing "domain wall", which means a very thin spherical shell of stressenergy. In this model, the grey line in DrGreg's diagram *would* indeed be the entire "collapsing matter", since that matter is supposed to be very thin. Obviously this is much less realistic, physically, than the collapse of spherically symmetric dust as in the standard OS type model (which itself is highly idealized, of course, with zero pressure and perfect spherical symmetry). They appear to be willing to make the educated guess that the qualitative conclusions from their model would still hold in a more realistic model; but they don't actually show that. However, that leaves a very big open question in my mind: what is *inside* the domain wall? The classical GR conclusion would be that it is a flat Minkowski spacetime region, which would shrink as the domain wall collapses. However, I don't see such a region included in the Krauss paper's model at all. I haven't read any of the papers making counterarguments, so I don't know if this issue has been raised. Just off the top of my head, including the flat region interior to the domain wall, if the conclusion of Krauss et al. is true that quantum effects stop the collapse by converting the domain wall's stressenergy into outgoing radiation before it forms a horizon, would change the whole spacetime diagram; it would no longer look like DrGreg's. (Actually, if Krauss et al. are correct and a horizon doesn't form when quantum effects are included, that would change the diagram in any case; the 45 degree line up and to the right is the horizon, and if there is no horizon that changes the whole causal structure.) This is probably getting pretty far off topic for this thread, though. 


#81
Nov1812, 09:58 PM

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Without radiation, and without a horizon, you could still the geometry as a large part of Dr. Greg's pink region. The grey line would bend up below the 'horizon that isn't there'. Anything outside (left of) the grey line would not be SC geometry, and we could cover it with a different chart. However, the remaining pink part could still represent the exact SC geometry outside the noncollapsing shell. 


#82
Nov1812, 10:49 PM

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#83
Nov1812, 10:59 PM

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#84
Nov1812, 11:09 PM

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#85
Nov1812, 11:36 PM

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#86
Nov1912, 12:05 AM

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#87
Nov1912, 10:59 AM

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But probably we will discuss that in your new thread, http://www.physicsforums.com/showthread.php?t=652839 


#88
Nov1912, 12:51 PM

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But again, as seem so common, I am not sure I understand what your are getting at. Probability of this seems 99% bidirectional between us. 


#89
Nov2112, 07:09 AM

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#90
Nov2312, 03:09 AM

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Voyager 35 is sent to a newly discovered black hole only about 20 light years away and which for simplicity we assume to be eternal static, and in rest wrt the solar system. The Voyager is indestructible and always in operation. A time code is emitted from Earth that can be received by Voyager. Voyager emits its proper time code s1 that is sent back to Earth together with the then received time stamp t1 from Earth (we'll ignore the technical difficulties). An observer on Earth with the name Kraus calculates the expected (s1,t1) signal from Voyager as function of expected UTC, for the approximation or assumption that the black hole is completely formed. He stresses that he could choose other coordinates, but that the "SC" of OppenheimerSnyder1939 are fine and valid for making predictions about what can be observed on Earth, making small corrections for Earth's gravitational field and orbit. He finds something like the following (I pull this out of my hat, just for the gist of it): UTC , (s1 , t1)  100 , 40.3, 200 1E3 , 41.2, 1.5E3 1E4 , 41.5, 1E5 1E5 , 41.7, 1E7 1E6 , 41.9, 1E10 1E100 42.0, 1E1000 My question: Please give an illustration of time codes t1 from Earth that reach Voyager at τ=43, as it has gone through the horizon. 


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