
#73
Nov2112, 02:24 AM

P: 3,178

However, the confusion between the time of observation here and the time of occurrence there is itself a recurring phenomenon in recent discussions; hopefully it will be settled in the thread on simultaneity. 



#74
Nov2112, 05:07 PM

P: 97

But this isn't physics. It is just the use of language. Mike 



#75
Nov2112, 06:00 PM

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PF Gold
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#76
Nov2112, 10:51 PM

P: 181

I have been following the discussions above, and somehow it has given rise to a new question in my mind:
I believe Einstein never quite accepted this particular corollary of GR, and he was not necessarily right in doing so. All the development of black hole theory seems to be postEinstein or extraEinstein... Any insights on this will be very helpful, especially if there is a chronology of the development of this. 



#77
Nov2112, 11:07 PM

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PF Gold
P: 5,503

1915: Einstein publishes his field equation. 1916: Schwarzschild discovers his solution, but he writes it in coordinates in which what we now know as the event horizon is at "r" = 0, not r = 2M. Consequently, he only discusses one region of the solution, whereas we now know (see below) that there are others as well. 1920's or early 30's: I believe Eddington, sometime during this period, came up with at least a version of what we now call EddingtonFinkelstein coordinates, but there was no followup for several decades. Also, sometime during this period, what we now call Painleve or Lemaitre coordinates were independently invented several times, but again there was no followup for several decades. 1939: Oppenheimer and Snyder publish their paper on gravitational collapse: first known model that includes collapsing matter and the vacuum region around it. However, they write their model in what we now call Schwarzschild exterior coordinates (*not* the same coordinates that Schwarzschild himself used in his 1916 paper!), and the physical nature of the coordinate singularity at the horizon (r = 2M) is not fully understood. 1939: Einstein publishes a paper showing that no stationary configuration of matter can be in a stable equilibrium unless its radius is at least 9/4 M (i.e., at least 9/8 of the Schwarzschild radius corresponding to its mass). He believes that this shows that gravitational collapse cannot occur; our modern understanding is that it only shows that a collapsing object, such as the one that appears in the OppenheimerSnyder paper, can't be in a stable equilibrium once its radius is less than 9/4 M. 1957: Finkelstein publishes a paper deriving what we now call EddingtonFinkelstein coordinates, and arguing that his derivation shows that the Schwarzschild solution to the Einstein Field Equation must include a region inside the event horizon, because otherwise the solution is incomplete: geodesics reach the horizon in a finite proper time, and all physical invariants are finite there, so they can't just stop without violating the EFE. 1960: Kruskal discovers that the full, maximally extended Schwarzschild solution contains even *more* regions than Finkelstein had thought: a total of four. Two of these (exterior, and black hole interior) are those covered by EddingtonFinkelstein (and Painleve) coordinates. However, Kruskal shows, by the same sorts of arguments that Finkelstein used, that in the (idealized and not physically reasonable, according to the best current understanding) case of a spherically symmetric spacetime which is vacuum everywhere, the solution is incomplete unless a "white hole" region and a *second* exterior region are also added. (These regions do *not* appear in solutions such as the OppenheimerSnyder model when those solutions are completed; instead, portions of regions I and II are joined to a nonvacuum region containing the collapsing matter.) 1960's: The "golden age" of black hole research: new mathematical tools are developed to study the global properties of spacetimes (i.e., solutions to the EFE), and various singularity theorems are proved which show that, if classical GR is correct, gravitational collapse starting from some reasonable initial conditions *must* form an event horizon, a black hole, and a curvature singularity at r = 0. After this point the study of black holes became "mainstream" relativity physics. 



#78
Nov2112, 11:10 PM

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PF Gold
P: 4,860

http://en.wikipedia.org/wiki/Timelin...k_hole_physics Plenty is missing, codiscoverers, and earlier discoverers often absent, but a reasonable high level chronology. Yes, Einstein never accepted that BH could actually form (he did not reject that they were solutions of GR). However, since all of Penrose and Hawking's work that really established they could and would form if GR is true came after his death, that isn't saying much. 



#79
Nov2212, 12:19 AM

P: 181

PeterDonis and PAllen,
This is great stuff. Thanks for the responses. This is very helpful. One more question this raises  does this mean that the original Schwarzschild solution/metric: 1/√(12GM/Rc^{2}  v^{2}/c^{2}  ...) or the c^{2}dτ^{2} = ... is no longer considered completely adequate, and has been superceded by later work? I believe the Schwarzschild solution is still used often, and describes some observed time dilation phenomena nicely (e.g. GPS satellites). Have there been further developments/refinements to this metric, and if so, would you be able to provide some inputs on that? Looking for something of low mathematical complexity that I can understand, not something marinated in tensors etc. hopefully ) 



#80
Nov2212, 03:46 AM

P: 3,178

This is very interesting indeed. :)
In view of the history I distinguish different "flavours" of GR:  1916 GR. Acceleration is truly "relative", and can be explained away by "induced gravitational fields". This was the driving force behind GR and it gave GR its name.  Early GR, or Einstein's GR. Even Einstein seems to have abandoned 1916 GR; however he stuck to the remainder, incl. the physical reality of gravitational fields.  Modern GR. It proposes the falling of matter inside R of black holes as well as the existence of white holes. However, modern GR is only partially accepted: white holes are found to violate thermodynamics (says Hamilton; I never looked at that). And the falling of matter inside R violates quantum mechanics. PS looking at the development like this from a distance, it appears that an equation has been pushed beyond its limits. 



#81
Nov2212, 09:28 AM

Physics
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PF Gold
P: 5,503

Every equation in any physical theory has solutions that aren't physically reasonable; as PAllen and I have pointed out in the other thread that's running on this topic, and as you agreed there, you have to add additional constraints to determine which mathematical solutions are physically reasonable. If you are going to make claims about what "modern GR" says, at least make them about what the full theory, including constraints as well as mathematical solutions to equations, actually says. 



#82
Nov2212, 11:08 AM

P: 3,178

 http://casa.colorado.edu/~ajsh/schww.html 



#83
Nov2312, 12:43 AM

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PF Gold
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#84
Nov2312, 01:59 AM

P: 3,178




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