Gravitation

General relativity

Mathematical physics

Wormhole

Equipotential surface

Quantum mechanics

Event horizon

Classical mechanics

Perturbation (astronomy)

Schwarzschild radius

Schwarzschild metric

Deriving the Schwarzschild solution

Kerr metric

Physics

Event (particle physics)

Physical Review

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 ${g}_{00}=0$. 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.

Event Horizons in Static Vacuum Space-Times