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 g₀₀=constant, the Schwarzschild solution is the only one which has a nonsingular infinite-red-shift surface g₀₀=0. 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.