A question about Snyder calculation of imploding stars(1939)

• Born2Perform
In summary, Oppenheimer and Snyder's idealized model of gravitational collapse showed that the surface of imploding stars, viewed by a static external observer, appears to freeze when it nears the horizon circumference. This has been confirmed by subsequent work and is supported by gtr. While there is some confusion in verbal summaries of this model, it is widely accepted that gtr predicts the formation of black holes in certain situations. The question of how we can see black holes when the surface takes an infinite amount of time to cross the horizon is best understood through visual aids and a strong mathematical background. The book "General Relativity from A to B" by Geroch provides a helpful explanation of black holes through pictures.
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

This is being discussed in several recent threads right now.

Oppenheimer-Snyder model of gravitational collapse

Hi, Born2Perform,

Born2Perform said:
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.

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.

Born2Perform said:
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.

Born2Perform said:
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

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What is the Snyder calculation of imploding stars(1939)?

The Snyder calculation of imploding stars was a theoretical model proposed by the physicist Howard P. Snyder in 1939 to explain the phenomenon of supernova explosions. It attempted to describe how the gravitational collapse of a massive star could generate enough energy to create a massive explosion.

What was the significance of the Snyder calculation of imploding stars(1939)?

The Snyder calculation was significant because it was one of the first attempts to mathematically explain the mechanism behind supernova explosions. It also laid the foundation for further research and theories on stellar evolution and the life cycle of stars.

Has the Snyder calculation of imploding stars(1939) been proven to be accurate?

No, the Snyder calculation has not been proven to be completely accurate. While it provided important insights into supernova explosions, further research and observations have shown that it is an oversimplified model and does not fully explain the complexities of stellar implosion and explosion.

What were some limitations of the Snyder calculation of imploding stars(1939)?

One major limitation of the Snyder calculation was that it did not take into account the effects of quantum mechanics and the behavior of matter under extreme conditions. It also did not consider the complexities of nuclear reactions and energy transport within the star.

How has the study of supernovae evolved since the Snyder calculation of imploding stars(1939)?

Since 1939, the study of supernovae has progressed significantly with advancements in technology and observational techniques. New models and theories have been proposed, and the understanding of supernova explosions has greatly improved. The Snyder calculation remains an important milestone in the history of supernova research, but it has been surpassed by more sophisticated models.

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