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

Helmut Friedrich, I. Rácz, Robert M. Wald

Research output: Contribution to journalArticle

108 Citations (Scopus)

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 geodesies. 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.

Original languageEnglish
Pages (from-to)691-707
Number of pages17
JournalCommunications in Mathematical Physics
Volume204
Issue number3
Publication statusPublished - 1999

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event horizon
rigidity
Rigidity
Cauchy
horizon
Horizon
theorems
Space-time
Null
Theorem
Black Holes
Killing Vector Field
Geodesies
generators
Geodesic
Hypersurface
Generator
Closed
Generalise

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon. / Friedrich, Helmut; Rácz, I.; Wald, Robert M.

In: Communications in Mathematical Physics, Vol. 204, No. 3, 1999, p. 691-707.

Research output: Contribution to journalArticle

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