How Fundamental Is General Relativity in Understanding Black Holes?

[lalbatros]

Dear all,

The possibility of black holes can be traced back to a special solution of the Einstein's equations, the famous Schwarzschild metric in 1916.

I find this very impressive, since at that time, the GR was a very young theory and it would have been more than natural to be skeptic about such a solution and the theory that leads to this solution.

I would like to know which aspects of GR, which 'ingredients', are the root cause for the Schwarzschild solution and the discovery of black holes. Or in other words, how much of GR is needed to come to the idea of black holes.

Am I right to say that clocks slowing down in a gravitational field is a consequence of the equivalence principle and SR? And would it be right the say that black holes are the consequence of that in the limit of large gravitational fields? Could the Schwarzschild radius be derived from such a simple analysis, and how justified could it be?

Michel

 

[pervect]

There was quite a bit of skepticism about black holes, and our understanding of them has improved considerably from the early days.

For instance, in some of the early papers, it was thought that the event horizon was a singularity of some sort, rather than an ill-behaved coordinate system. Also, early views of "black holes" tended to view them as "frozen stars".

To actually solve the metric for black holes, one needs the complete Einstein field equations, G_uv = 8 pi T_uv, that relate curvature to matter density.

I'm not sure how much one can derive about their proprerties using only the equivalence principle, unfortunately.

 

[Entropia]

,

Thank you for sharing this interesting information about the origins of black holes. I agree that it is quite impressive that the concept of black holes can be traced back to a solution of Einstein's equations in 1916, at a time when the theory of general relativity was still in its infancy. It speaks to the genius of Einstein and the power of his theory to predict such a phenomenon.

To answer your questions, the Schwarzschild solution is a direct consequence of the Einstein field equations, which are the fundamental equations of general relativity. These equations describe the curvature of spacetime in the presence of matter and energy. The ingredients needed for the Schwarzschild solution are the mass of the object and the distance from the center of the object. In this sense, black holes can be seen as a direct consequence of the principles of general relativity.

You are correct in saying that the slowing of clocks in a gravitational field is a consequence of the equivalence principle and special relativity. The equivalence principle states that the effects of gravity are equivalent to the effects of acceleration. And special relativity predicts that time will slow down for an observer in a gravitational field compared to an observer in a non-gravitational field. This effect is also known as gravitational time dilation.

In the limit of very strong gravitational fields, such as those near a black hole, the time dilation becomes extreme and can lead to the formation of an event horizon, which is the boundary of a black hole. The Schwarzschild radius is the distance from the center of a black hole at which the escape velocity is equal to the speed of light. This radius can be derived from the equations of general relativity and is a fundamental property of black holes.

In summary, the concepts of black holes are deeply rooted in the principles of general relativity, particularly the equations that describe the curvature of spacetime in the presence of mass and energy. The equivalence principle and special relativity also play important roles in understanding the behavior of black holes. I hope this helps to answer your questions. Thank you again for sharing your thoughts on this topic.