Journal Article10.1103/PHYSREV.164.1776
Event Horizons in Static Vacuum Space-Times
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TL;DR: 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.
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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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References
Stability of a Schwarzschild Singularity
TL;DR: In this article, it was shown that a Schwarzschild singularity, spherically symmetrical and endowed with mass, will undergo small vibrations about the spherical form and therefore remain stable if subjected to a small nonspherical perturbation.
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Maximal analytic extension of the Kerr metric
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Collinear particles and bondi dipoles in general relativity
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