Is there a mathematical proof for the existance of black hole.
Black holes are predicted by General Relativity, yes.
Math can't "prove" anything actually exists.
But, gather enough mass in one place, and GR says it must collapse into a BH (assuming it's collapse is not held at bay by fusion, such as in an active star). It's pretty much that simple.
We do have observations of masses that large and larger, and we know that they must be contained in a volume of limited size (we can tell by things orbiting it). So whatever is there, pretty much has to be a BH.
Uh ... Einstein's General Relativity equations?
Is it related to the Schwarzschild solution for the einsteins field equation
. From existance I mean prediction or assumption
If you mean, does that solution describe a black hole, yes, it does.
Thank you peterdonis
Thanks for every one
A person had posted a pdf related to the solution of efe, that was really awsom , thank u man for that wonderful pdf
If the math in that reference is helpful to you, that's good. Please bear in mind, though, that the moderators have reviewed the reference and determined that it contains misstatements (not in the mathematical derivation, in the non-mathematical background given in the early part of the thesis) that make it unsuitable for use as a reference here. So you should be careful in what you take from the discussion in that reference (apart from the mathematical derivation given).
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