# Einsteins equation : Black hole solution

Let Einstein's equations satisfy $R_{\mu \nu } = 0$. Suppose we solve it numerically with the aid of a computer. Can we know from the numerical solution if there is a black HOle in the solutions? For example, how can you know when you solve Einstein's equation if your solution will be a black hole or other particular non-smooth solution?

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Did you mean $R_{\mu\nu} = 0$? That would normally mean the Ricci tensor is zero i.e. the space is Ricci flat, so there couldn't be any horizons or singularities. – John Rennie Sep 3 '12 at 14:14
@JohnRennie: the Kerr solution is Ricci flat. All $R_{\mu \nu}=0$ tells you is that you don't have any matter. – Jerry Schirmer Sep 3 '12 at 14:56
Just an addition to Jerry's comment; John, you may have confused Ricci flatness and Riemann flatness. Riemann flatness - literally (piecewise) flat Minkowski spacetime - requires $R_{\kappa\lambda\mu\nu}=0$, not just $R_{\mu\nu}=0$. The former condition is stronger and implies the latter but not vice versa. – Luboš Motl Sep 3 '12 at 15:00
@JerrySchirmer and Luboš: thanks, this site teaches me something new every day :-) – John Rennie Sep 3 '12 at 17:06