Regularity of Horizons and the Area Theorem (Preprint)
Abstract
We prove that the area of section 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 exist a conformal completion with a "H-regular" Scri plus ; 3) the horizon is a black hole event in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established. This extends to 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 sigh are made. We provide 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 the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 14, 2000
- Accession Number
- ADA640822
Entities
People
- Erwann Delay
- Gregory J. Galloway
- Piotr T. Chrusciel
- Ralph Howard
Organizations
- University of South Carolina