Find Solutions to Black Hole Questions

[sadegh4137]

hi
if you want to find the black hole solutions, what do you do?
has any solutions of $R_\alpha\beta=0$ a black hole?

thanks

 

[Nugatory]

hi
if you want to find the black hole solutions, what do you do?
has any solutions of $$R_\alpha\beta=0$$ a black hole?

Google for "Schwarzschild Solution" and "Schwarzschild Radius".

 

[George Jones]

Uncharged spherical (Schwarzschild) and rotating (Kerr) black holes are vacuum solutions, i.e., have $$R_{\alpha\beta} = 0.$$

 

[WannabeNewton]

has any solutions of $R_\alpha\beta=0$ a black hole?

As stated above, there are black hole solutions which solve the vacuum Einstein equations but the converse, as you have stated it, is clearly not true (a vacuum solution need not be a black hole solution). Just take the trivial solution (Minkowski space-time) as a counterexample.

 

[George Jones]

And there are black hole solutions that are not vacuum solutions, e.g., Reissner-Nordstrom and Kerr-Newman black holes (these are electrovac solutions).

 

[sadegh4137]

thanks
how you can recognize a metric is a black hole or not?
or how you can find black hole solution?
at first you find vacuum solution of Einstein equations?
and then?