Black holes in static vacuum spacetimes
Abstract
An extension of Israel's theorem on the regularity of Killing horizons is proven. Well behaved asymptotically flat vacuum solutions of the Einstein equations which represent the exterior of a nonrotating black hole are considered. It is shown that the black hole has spherical topology and that the equipotential surfaces g _{00}=constant are nonintersecting twospheres. The solutions must therefore be members of the oneparameter family of spherically symmetric Schwarzschild solutions.
 Publication:

General Relativity and Gravitation
 Pub Date:
 February 1973
 DOI:
 10.1007/BF00769760
 Bibcode:
 1973GReGr...4...53H