Trapped surfaces and symmetries

Classical and Quantum Gravity

Volumn 20, Issue 24, 2003, Pages

  Mars, Marc ^a   Senovilla, José M M ^b  

^a UNIVERSITY OF SALAMANCA   (Spain)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346991473     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/20/24/L03     Document Type: Article

References (42)

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5. Demni P. N. and Janis A. I. 1973 The characteristic development of trapped surfaces J. Math. Phys. 14 793 Alfes U. and Müler zum Hagen H. 1994 Spherically symmetric event horizons and trapped surfaces developing from innocuous data Class. Quantum Grav. 11 2705 Beig R. and Ó Murchadha N. 1994 Trapped surfaces in vacuum spacetimes Class. Quantum Grav. 11 419 Beig R. and Ó Murchadha N. 1996 Vacuum spacetimes with future trapped surfaces Class. Quantum Grav. 13 739 Bizon P., Malec E. and Ó Murchadha N. 1989 Trapped surfaces due to concentration of matter in spherically symmetric geometries Class. Quantum Grav. 7 961
6. Demni P. N. and Janis A. I. 1973 The characteristic development of trapped surfaces J. Math. Phys. 14 793 Alfes U. and Müler zum Hagen H. 1994 Spherically symmetric event horizons and trapped surfaces developing from innocuous data Class. Quantum Grav. 11 2705 Beig R. and Ó Murchadha N. 1994 Trapped surfaces in vacuum spacetimes Class. Quantum Grav. 11 419 Beig R. and Ó Murchadha N. 1996 Vacuum spacetimes with future trapped surfaces Class. Quantum Grav. 13 739 Bizon P., Malec E. and Ó Murchadha N. 1989 Trapped surfaces due to concentration of matter in spherically symmetric geometries Class. Quantum Grav. 7 961
7. Demni P. N. and Janis A. I. 1973 The characteristic development of trapped surfaces J. Math. Phys. 14 793 Alfes U. and Müler zum Hagen H. 1994 Spherically symmetric event horizons and trapped surfaces developing from innocuous data Class. Quantum Grav. 11 2705 Beig R. and Ó Murchadha N. 1994 Trapped surfaces in vacuum spacetimes Class. Quantum Grav. 11 419 Beig R. and Ó Murchadha N. 1996 Vacuum spacetimes with future trapped surfaces Class. Quantum Grav. 13 739 Bizon P., Malec E. and Ó Murchadha N. 1989 Trapped surfaces due to concentration of matter in spherically symmetric geometries Class. Quantum Grav. 7 961
8. Demni P. N. and Janis A. I. 1973 The characteristic development of trapped surfaces J. Math. Phys. 14 793 Alfes U. and Müler zum Hagen H. 1994 Spherically symmetric event horizons and trapped surfaces developing from innocuous data Class. Quantum Grav. 11 2705 Beig R. and Ó Murchadha N. 1994 Trapped surfaces in vacuum spacetimes Class. Quantum Grav. 11 419 Beig R. and Ó Murchadha N. 1996 Vacuum spacetimes with future trapped surfaces Class. Quantum Grav. 13 739 Bizon P., Malec E. and Ó Murchadha N. 1989 Trapped surfaces due to concentration of matter in spherically symmetric geometries Class. Quantum Grav. 7 961
9. Demni P. N. and Janis A. I. 1973 The characteristic development of trapped surfaces J. Math. Phys. 14 793 Alfes U. and Müler zum Hagen H. 1994 Spherically symmetric event horizons and trapped surfaces developing from innocuous data Class. Quantum Grav. 11 2705 Beig R. and Ó Murchadha N. 1994 Trapped surfaces in vacuum spacetimes Class. Quantum Grav. 11 419 Beig R. and Ó Murchadha N. 1996 Vacuum spacetimes with future trapped surfaces Class. Quantum Grav. 13 739 Bizon P., Malec E. and Ó Murchadha N. 1989 Trapped surfaces due to concentration of matter in spherically symmetric geometries Class. Quantum Grav. 7 961
10. Penrose R 1969 Gravitational collapse: the role of general relativity Nuovo Cimento 1 252 Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068 Christodoulou D 1999 The instability of naked singularities in the gravitational collapse of a scalar field Ann. Math. 149 183 Królak A 1986 Towards the proof of the cosmic censorship hypothesis Class. Quantum Grav. 3 267 Chrusćiel P T, Isenberg J and Moncrief V 1990 Strong cosmic censorship in polarized Gowdy spacetimes Class. Quantum Grav. 7 1671 Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
11. Penrose R 1969 Gravitational collapse: the role of general relativity Nuovo Cimento 1 252 Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068 Christodoulou D 1999 The instability of naked singularities in the gravitational collapse of a scalar field Ann. Math. 149 183 Królak A 1986 Towards the proof of the cosmic censorship hypothesis Class. Quantum Grav. 3 267 Chrusćiel P T, Isenberg J and Moncrief V 1990 Strong cosmic censorship in polarized Gowdy spacetimes Class. Quantum Grav. 7 1671 Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
12. Penrose R 1969 Gravitational collapse: the role of general relativity Nuovo Cimento 1 252 Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068 Christodoulou D 1999 The instability of naked singularities in the gravitational collapse of a scalar field Ann. Math. 149 183 Królak A 1986 Towards the proof of the cosmic censorship hypothesis Class. Quantum Grav. 3 267 Chrusćiel P T, Isenberg J and Moncrief V 1990 Strong cosmic censorship in polarized Gowdy spacetimes Class. Quantum Grav. 7 1671 Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
13. Penrose R 1969 Gravitational collapse: the role of general relativity Nuovo Cimento 1 252 Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068 Christodoulou D 1999 The instability of naked singularities in the gravitational collapse of a scalar field Ann. Math. 149 183 Królak A 1986 Towards the proof of the cosmic censorship hypothesis Class. Quantum Grav. 3 267 Chrusćiel P T, Isenberg J and Moncrief V 1990 Strong cosmic censorship in polarized Gowdy spacetimes Class. Quantum Grav. 7 1671 Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
14. Penrose R 1969 Gravitational collapse: the role of general relativity Nuovo Cimento 1 252 Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068 Christodoulou D 1999 The instability of naked singularities in the gravitational collapse of a scalar field Ann. Math. 149 183 Królak A 1986 Towards the proof of the cosmic censorship hypothesis Class. Quantum Grav. 3 267 Chrusćiel P T, Isenberg J and Moncrief V 1990 Strong cosmic censorship in polarized Gowdy spacetimes Class. Quantum Grav. 7 1671 Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
15. Penrose R 1969 Gravitational collapse: the role of general relativity Nuovo Cimento 1 252 Wald R 1997 Gravitational collapse and cosmic censorship Preprint gr-qc/9710068 Christodoulou D 1999 The instability of naked singularities in the gravitational collapse of a scalar field Ann. Math. 149 183 Królak A 1986 Towards the proof of the cosmic censorship hypothesis Class. Quantum Grav. 3 267 Chrusćiel P T, Isenberg J and Moncrief V 1990 Strong cosmic censorship in polarized Gowdy spacetimes Class. Quantum Grav. 7 1671 Dafermos M 2003 The interior of charged black holes and the problem of uniqueness in general relativity Preprint gr-qc/0307013
16. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
17. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
18. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
19. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
20. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
21. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
22. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
23. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
24. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
25. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
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27. Penrose R 1973 Naked singularities Ann. New York Acad. Sci. 224 125 Gibbons G 1997 Collapsing shells and the isoperimetric inequality Class. Quantum Grav. 14 2905 Huisken G and Ilmanen T 2001 The inverse mean curvature flow and the Riemannian Penrose inequality J. Diff. Geom. 59 353 Bray H 2001 Proof of the Riemannian Penrose inequality using the positive mass theorem J. Diff. Geom. 59 177 Geroch R 1973 Energy extraction Ann. New York Acad. Sci. 224 108 Jang P S and Wald R 1977 The positive energy conjecture and the cosmic censorship J. Math. Phys. 18 41 Herzlich M 1997 A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds Commun. Math. Phys. 188 121 Malec E, Mars M and Simon W 2002 On the Penrose inequality for general horizons Phys. Rev. Lett. 88 121102 Ludvigsen M and Vickers JAG 1983 An inequality relating total mass and the area of a trapped surface in general relativity J. Phys. A: Math. Gen. 16 3349 Bergqvist G 1997 On the Penrose inequality and the role of auxiliary spinor fields Class. Quantum Grav. 14 2577 Malec E and Ó Murchadha N 1994 Trapped surfaces and the Penrose inequality in spherically symmetric geometries Phys. Rev. D 49 6931 Hayward S A 1994 Quasi-localization of Bondi-Sachs energy-loss Class. Quantum Grav. 11 3037
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