Regularity of Horizons and The Area Theorem

Details Regularity of Horizons and The Area Theorem Regularity of Horizons and The Area Theorem

2000-01-03

arxiv.org/abs/gr-qc/0001003v2

Annales Henri Poincare 2 (2001) 109-178

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

final version to appear in Annales Henri Poincare, various changes as suggested by a referee, in particular a section on Krola

Scientific paper

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 any one of 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 ``H-regular'' Scri plus; 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. No assumptions about the cosmological constant or its sign are made. 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.

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