Event Horizons in Static Vacuum Space-Times
W. IsraelMathematics Department, University of Alberta, Alberta, Canada and Dublin Institute for Advanced Studies, Dublin, Ireland
1967en
ABI
Abstract
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.
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