Piotr T. Chrusciel,
Gregory J. Galloway,
Comments: Here is the final version of our joint paper with E.Delay, G.Galloway, and R.Howard on the area theorem, accepted for publication in Annales Henri Poincare. The files 00* correspond to the original gr-qc/0001003 submission; the files area* are an update thereof, with several corrections and extensions following comments by an anonymous referee. In particular the original title "The Area Theorem" has become "Regularity of Horizons and the Area Theorem"; further, it is shown that Krolak's area theorems hold without differentiability hypotheses on the horizon.
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.
Listing of Tue Dec 12 23:04:57 CET 2000:
|0001003.pdf||(May 27 2000)||776438|
|0001003.ps||(May 27 2000)||1335683|
|0001003v2.pdf||(May 27 2000)||776597|
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|area12XII2000.dvi||(Dec 12 22:23)||411020|
|area12XII2000.ps||(Dec 12 22:23)||910385|
|area12XII2000.tex||(Dec 12 22:23)||260185|