On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon

Friedrich, H. and Rácz, István and Wald, R. M. (1999) On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 204. pp. 691-707. ISSN 0010-3616

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Abstract

We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively, the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is non-degenerate in the sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon. We thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the non-analytic case.

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