Abstract
The following theorem is established. Among all static, asymptotically flat vacuum space-times with closed simply connected equipotential surfaces , the Schwarzschild solution is the only one which has a nonsingular infinite-red-shift surface . Thus there exists no static asymmetric perturbation of the Schwarzschild manifold due to internal sources (e.g., a quadrupole moment) which will preserve a regular event horizon. Possible implications of this result for asymmetric gravitational collapse are briefly discussed.
- Received 27 April 1967
DOI:https://doi.org/10.1103/PhysRev.164.1776
©1967 American Physical Society