Event Horizons in Static Vacuum Space-Times

The following theorem is established. Among all static, asymptotically flat vacuum space-times with closed simply connected equipotential surfaces $g_{00}=\mathrm{constant}$, the Schwarzschild solution is the only one which has a nonsingular infinite-red-shift surface $g_{00}=0\mathrm{}$. 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.