### 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 language | English |
---|---|

Pages (from-to) | 691-707 |

Number of pages | 17 |

Journal | Communications in Mathematical Physics |

Volume | 204 |

Issue number | 3 |

Publication status | Published - 1999 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*204*(3), 691-707.

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

Research output: Article

*Communications in Mathematical Physics*, vol. 204, no. 3, pp. 691-707.

}

TY - JOUR

T1 - On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon

AU - Friedrich, Helmut

AU - Rácz, I.

AU - Wald, Robert M.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033245376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033245376&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033245376

VL - 204

SP - 691

EP - 707

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -