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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Received: 4 November 1998 / Accepted: 13 February 1999
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Friedrich, H., Rácz, I. & Wald, R. On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon. Comm Math Phys 204, 691–707 (1999). https://doi.org/10.1007/s002200050662
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DOI: https://doi.org/10.1007/s002200050662