### Abstract

We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\cal H} $-regular" $ {\cal J} $^{+}; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.

Original language | English (US) |
---|---|

Pages (from-to) | 109-178 |

Number of pages | 70 |

Journal | Annales Henri Poincare |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Feb 1 2001 |

### Fingerprint

### Keywords

- Black Hole
- Energy Condition
- Event Horizon
- Future Event
- Relevant Part

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Annales Henri Poincare*,

*2*(1), 109-178. https://doi.org/10.1007/PL00001029

**Regularity of Horizons and the Area Theorem.** / Chruściel, Piotr T.; Delay, Erwann; Galloway, Gregory J.; Howard, Ralph.

Research output: Contribution to journal › Article

*Annales Henri Poincare*, vol. 2, no. 1, pp. 109-178. https://doi.org/10.1007/PL00001029

}

TY - JOUR

T1 - Regularity of Horizons and the Area Theorem

AU - Chruściel, Piotr T.

AU - Delay, Erwann

AU - Galloway, Gregory J.

AU - Howard, Ralph

PY - 2001/2/1

Y1 - 2001/2/1

N2 - We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\cal H} $-regular" $ {\cal J} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.

AB - We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\cal H} $-regular" $ {\cal J} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.

KW - Black Hole

KW - Energy Condition

KW - Event Horizon

KW - Future Event

KW - Relevant Part

UR - http://www.scopus.com/inward/record.url?scp=23044526747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044526747&partnerID=8YFLogxK

U2 - 10.1007/PL00001029

DO - 10.1007/PL00001029

M3 - Article

AN - SCOPUS:23044526747

VL - 2

SP - 109

EP - 178

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 1

ER -