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} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 109-178 |
| Number of pages | 70 |
| Journal | Annales Henri Poincare |
| Volume | 2 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 1 2001 |
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Keywords
- Black Hole
- Energy Condition
- Event Horizon
- Future Event
- Relevant Part
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
Cite this
Regularity of Horizons and the Area Theorem. / Chruściel, Piotr T.; Delay, Erwann; Galloway, Gregory J.; Howard, Ralph.
In: Annales Henri Poincare, Vol. 2, No. 1, 01.02.2001, p. 109-178.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Regularity of Horizons and the Area Theorem
AU - Chruściel, Piotr T.
AU - Delay, Erwann
AU - Galloway, Gregory J.
AU - Howard, Ralph
PY - 2001/2/1
Y1 - 2001/2/1
N2 - We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\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 -