# Black hole solutions

1. Jul 19, 2013

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

2. Jul 19, 2013

### Staff: Mentor

3. Jul 19, 2013

### George Jones

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

4. Jul 19, 2013

### WannabeNewton

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.

5. Jul 19, 2013

### George Jones

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

6. Jul 20, 2013