Regularity of Horizons and the Area Theorem
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...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chruściel, Piotr T. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2001 |
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| Schlagwörter: |
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| Anmerkung: |
© Birkhäuser Verlag Basel, 2001 |
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| Übergeordnetes Werk: |
Enthalten in: Annales Henri Poincaré - Birkhäuser-Verlag, 2000, 2(2001), 1 vom: 01. Feb., Seite 109-178 |
|---|---|
| Übergeordnetes Werk: |
volume:2 ; year:2001 ; number:1 ; day:01 ; month:02 ; pages:109-178 |
| Links: |
|---|
| DOI / URN: |
10.1007/PL00001029 |
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OLC2058748026 |
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| 520 | |a 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} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons. | ||
| 650 | 4 | |a Black Hole | |
| 650 | 4 | |a Energy Condition | |
| 650 | 4 | |a Event Horizon | |
| 650 | 4 | |a Future Event | |
| 650 | 4 | |a Relevant Part | |
| 700 | 1 | |a Delay, Erwann |4 aut | |
| 700 | 1 | |a Galloway, Gregory J. |4 aut | |
| 700 | 1 | |a Howard, Ralph |4 aut | |
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10.1007/PL00001029 doi (DE-627)OLC2058748026 (DE-He213)PL00001029-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chruściel, Piotr T. verfasserin aut Regularity of Horizons and the Area Theorem 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag Basel, 2001 Abstract. We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\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. Black Hole Energy Condition Event Horizon Future Event Relevant Part Delay, Erwann aut Galloway, Gregory J. aut Howard, Ralph aut Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 2(2001), 1 vom: 01. Feb., Seite 109-178 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:2 year:2001 number:1 day:01 month:02 pages:109-178 https://doi.org/10.1007/PL00001029 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 GBV_ILN_4310 AR 2 2001 1 01 02 109-178 |
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10.1007/PL00001029 doi (DE-627)OLC2058748026 (DE-He213)PL00001029-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chruściel, Piotr T. verfasserin aut Regularity of Horizons and the Area Theorem 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag Basel, 2001 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. Black Hole Energy Condition Event Horizon Future Event Relevant Part Delay, Erwann aut Galloway, Gregory J. aut Howard, Ralph aut Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 2(2001), 1 vom: 01. Feb., Seite 109-178 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:2 year:2001 number:1 day:01 month:02 pages:109-178 https://doi.org/10.1007/PL00001029 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 GBV_ILN_4310 AR 2 2001 1 01 02 109-178 |
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10.1007/PL00001029 doi (DE-627)OLC2058748026 (DE-He213)PL00001029-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chruściel, Piotr T. verfasserin aut Regularity of Horizons and the Area Theorem 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag Basel, 2001 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. Black Hole Energy Condition Event Horizon Future Event Relevant Part Delay, Erwann aut Galloway, Gregory J. aut Howard, Ralph aut Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 2(2001), 1 vom: 01. Feb., Seite 109-178 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:2 year:2001 number:1 day:01 month:02 pages:109-178 https://doi.org/10.1007/PL00001029 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 GBV_ILN_4310 AR 2 2001 1 01 02 109-178 |
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10.1007/PL00001029 doi (DE-627)OLC2058748026 (DE-He213)PL00001029-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chruściel, Piotr T. verfasserin aut Regularity of Horizons and the Area Theorem 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag Basel, 2001 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. Black Hole Energy Condition Event Horizon Future Event Relevant Part Delay, Erwann aut Galloway, Gregory J. aut Howard, Ralph aut Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 2(2001), 1 vom: 01. Feb., Seite 109-178 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:2 year:2001 number:1 day:01 month:02 pages:109-178 https://doi.org/10.1007/PL00001029 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 GBV_ILN_4310 AR 2 2001 1 01 02 109-178 |
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10.1007/PL00001029 doi (DE-627)OLC2058748026 (DE-He213)PL00001029-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chruściel, Piotr T. verfasserin aut Regularity of Horizons and the Area Theorem 2001 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Birkhäuser Verlag Basel, 2001 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} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons. Black Hole Energy Condition Event Horizon Future Event Relevant Part Delay, Erwann aut Galloway, Gregory J. aut Howard, Ralph aut Enthalten in Annales Henri Poincaré Birkhäuser-Verlag, 2000 2(2001), 1 vom: 01. Feb., Seite 109-178 (DE-627)313331340 (DE-600)2011018-2 (DE-576)085108839 1424-0637 nnns volume:2 year:2001 number:1 day:01 month:02 pages:109-178 https://doi.org/10.1007/PL00001029 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_40 GBV_ILN_70 GBV_ILN_285 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4029 GBV_ILN_4277 GBV_ILN_4310 AR 2 2001 1 01 02 109-178 |
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Regularity of Horizons and the Area Theorem |
| abstract |
Abstract. We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\cal H} $-regular" $ {\cal J} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons. © Birkhäuser Verlag Basel, 2001 |
| abstractGer |
Abstract. We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\cal H} $-regular" $ {\cal J} $+; 3) the horizon is a black hole event horizon in a space-time which has a globally hyperbolic conformal completion. (Some related results under less restrictive hypotheses are also established.) This extends a theorem of Hawking, in which piecewise smoothness of the event horizon seems to have been assumed. We prove smoothness or analyticity of the relevant part of the event horizon when equality in the area inequality is attained – this has applications to the theory of stationary black holes, as well as to the structure of compact Cauchy horizons. In the course of the proof we establish several new results concerning the differentiability properties of horizons. © Birkhäuser Verlag Basel, 2001 |
| abstract_unstemmed |
Abstract. We prove that the area of sections of future event horizons in space-times satisfying the null energy condition is non-decreasing towards the future under the following circumstances: 1) the horizon is future geodesically complete; 2) the horizon is a black hole event horizon in a globally hyperbolic space-time and there exists a conformal completion with a "$ {\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. © Birkhäuser Verlag Basel, 2001 |
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| title_short |
Regularity of Horizons and the Area Theorem |
| url |
https://doi.org/10.1007/PL00001029 |
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| author2 |
Delay, Erwann Galloway, Gregory J. Howard, Ralph |
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Delay, Erwann Galloway, Gregory J. Howard, Ralph |
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| doi_str |
10.1007/PL00001029 |
| up_date |
2024-07-03T20:04:38.801Z |
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1803589599960760320 |
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