A question about Snyder calculation of imploding stars(1939)

[Born2Perform]

hi:
Using gr and with great idealizations he discovered that the surface of imploding stars, viewed by a static external observer, seems to freeze when its circumference nears the horizon circumference for that star.
If i am not wrong this was also confirmed by Wheeler's student Wakano several years after.

Probably i misunderstood something in those reports, but if not, how can we see black holes, if the surface takes an infinite amount of our time to cross the horizon? thank you

 

[pervect]

This is being discussed in several recent threads right now.

 

[Chris Hillman]

Oppenheimer-Snyder model of gravitational collapse

Hi, Born2Perform,

Using gr and with great idealizations [Oppenheimer and Snyder] discovered that the surface of imploding stars, viewed by a static external observer, seems to freeze when its circumference nears the horizon circumference for that star.

Two comments:

1. You mentioned "great idealizations". No doubt you refer to the fact that OS assumed a perfectly spherical collapse, and they assumed that the collapsing matter can be modeled as a "pressureless perfect fluid" or "dust". One could object that perhaps small asymmetries, or the pressure of a more realistic model of a collapsing supernova core (say) would change their conclusion. But much subsequent work has confirmed many times over that more realistic models confirm that complete gravitational collapse and the formation of a black hole is firmly predicted by gtr under appropriate conditions. Gtr might be wrong about this, of course, but that seems very unlikely at present; gtr is one of the best-tested theories of fundamental physics, and astronomers have uncovered some pretty convincing evidence that event horizons do exist in nature (this is the defining characteristic of a "black hole").

2. Some verbal summaries of the OS model do attempt to describe some features of the OS model by saying something like "the surface of imploding stars, viewed by a static external observer, seems to freeze when its circumference nears $$r=2m$$". This is confusing and misleading on many different levels, and is almost universally deprecated by modern textbook authors, and even by those authors of popular books, such as Thorne, Wald, and Geroch, who also happen to be leading experts on gtr. For an excellent discussion of the physical interpretation of the OS collapsing dust ball model, try the classic textbook Gravitation, by Misner, Thorne, and Wheeler.

If i am not wrong this was also confirmed by Wheeler's student Wakano several years after.

Well, HUNDREDS of papers on gravitational collapse models have appeared since 1939. In addition to these, a huge amount of work has been done on approximations to realistic analytical models, and on numerical simulations. All of these approaches encounter various difficulties, but they all tend to support one another in the basic conclusion: gtr firmly predicts the formation of black holes by gravitational collapse in various situations.

how can we see black holes, if the surface takes an infinite amount of our time to cross the horizon?

Well, of course gtr says no such thing. What gtr DOES say about this situation is in my opinion best understood in pictures. Here it is tremendously helpful to have a strong mathematical background, but this is not strictly speaking necessary if you have a strong visual imagination. The popular book by Geroch, General Relativity from A to B, has the goal of explaining black holes using only pictures, and in my opinion the author suceeds admirably!

Chris Hillman