A simple proof of the generalization of Israel's theorem

Details A simple proof of the generalization of Israel's theorem A simple proof of the generalization of Israel's theorem

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..695r&link_type=abstract

General Relativity and Gravitation, vol. 8, Aug. 1977, p. 695-698.

Astronomy and Astrophysics

Astronomy

44

Black Holes (Astronomy), Relativity, Schwarzschild Metric, Space-Time Functions, Einstein Equations, Theorem Proving, Topology, Vacuum

Scientific paper

Israel's (1967) theorem concerning the uniqueness of the Schwarzschild black hole states that a static regular predictable space-time corresponding to a vacuum solution of Einstein's field equations must be a positive-mass Schwarzschild solution if (1) past and future event horizons exist and intersect in a connected compact spacelike two-surface with the topology of a two-sphere and (2) the magnitude of the timelike hypersurface orthogonal Killing-vector field has a nonzero gradient in the static region exterior to the event horizons. A simple proof of this theorem is outlined which does not depend on the assumption of condition (2) and which avoids the technical complexity of a previous proof due to Mueller zum Hagen et al. (1973). Boundary and coordinate conditions are formulated, and two analytic properties of the Schwarzschild solution are used to demonstrate the uniqueness of the Schwarzschild black hole.

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