The classification of static vacuum spacetimes containing an asymptotically flat spacelike hypersurface with compact interior

Classical and Quantum Gravity

Volumn 16, Issue 3, 1999, Pages 661-687

  Chruściel, Piotr T ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033239512     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/16/3/004     Document Type: Article

References (50)

1. Anderson M T 1998 On the structure of solutions to the static vacuum Einstein equations Preprint
2. Ashtekar A and Magnon-Ashtekar A 1979 On conserved quantities in general relativity J. Math. Phys. 20 793-800
3. Bardeen J M, Carter B and Hawking S W 1973 The four laws of black hole mechanics Commun. Math. Phys. 31 161-70
4. Bartnik R and Chruściel P T 1998 in preparation
5. 00 Phys. Lett. A 69 153-5
6. Beig R 1991 Conformal properties of static spacetimes Class. Quantum Grav. 8 263-71
7. Beig R and Chruściel P T 1996 Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem J. Math. Phys. 37 1939-61
8. Beig R and Chruściel P T 1997 The isometry groups of asymptotically flat, asymptotically empty space-times with timelike ADM four-momentum Commun. Math. Phys. 188 585-97
9. Beig R and Simon W 1981 On the multipole expansion for stationary space-times Proc. R. Soc. A 376 333-41
10. Beig R and Simon W 1992 On the uniqueness of static perfect-fluid solutions in general relativity Commun. Math. Phys. 144 373-90
11. Boyer R H 1969 Geodesic Killing orbits and bifurcate Killing horizons Proc. R. Soc. A 311 245-52
12. Bunting G and Masood-ul-Alam A K M 1987 Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-time Gen. Rel. Grav. 19 147-54
13. Carter B 1969 Killing horizons and orthogonally transitive groups in space-time J. Math. Phys. 10 70-81
14. Carter B 1973 Black hole equilibrium states Proc. Les Houches Summer School (Black Holes) ed C de Witt and B de Wilt (New York: Gordon and Breach)
15. Chruściel P T 1986 A remark on the positive energy theorem Class. Quantum Grav. 33 L115-21
16. Chruściel P T 1994 'No hair' theorems - folklore, conjectures, results Differential Geometry and Mathematical Physics (Contemporary Mathematics vol 170) ed J Beem and K L Duggal (Providence, RI: American Mathematical Society) pp 23-49
17. Chruściel P T 1996 Uniqueness of black holes revisited Proc. Journées Relativistes 96 ed N Straumann, Ph Jetzer and G Lavrelashvili (Helv. Phys. Acta 69 529-52)
18. Chruściel P T 1996 Uniqueness of black holes revisited Proc. Journées Relativistes 96 ed N Straumann, Ph Jetzer and G Lavrelashvili (Helv. Phys. Acta 69 529-52)
19. Chruściel P T 1997 On rigidity of analytic black holes Commun. Math. Phys. 189 1-7
20. Chruściel P T 1998 A remark on differentiability of Cauchy horizons Class. Quantum Grav. 15 3845-8 (Chruściel P T 1998 A remark on differentiability of Cauchy horizons Preprint gr-qc/9807059)
21. Chruściel P T 1998 A remark on differentiability of Cauchy horizons Class. Quantum Grav. 15 3845-8 (Chruściel P T 1998 A remark on differentiability of Cauchy horizons Preprint gr-qc/9807059)
22. Chruściel P T 1999 Towards a classification of static electrovacuum spacetimes containing an asymptotically flat spacelike hypersurface with compact interior Class. Quantum Grav. 16 689-703
23. Chruściel P T and Nadirashvili N S 1995 All electrovacuum Majumdar-Papapetrou spacetimes with non-singular black holes Class. Quantum Grav. 12 L17-23
24. Chruściel P T and Wald R M 1994 Maximal hypersurfaces in stationary asymptotically flat space-times Commun. Math. Phys. 163 561-604
25. Chruściel P T and Wald R M 1994 On the topology of stationary black holes Class. Quantum Grav. 11 L147-52
26. Eells J and Ratto A 1993 Harmonic Maps and Minimal Immersions with Symmetries (Ann. Math. Studies vol 130) (Princeton, NJ: Princeton University Press)
27. Geroch R and Pemg S-M 1994 Total mass-momentum of arbitrary initial-data sets in general relativity J. Math. Phys. 35 4157-77
28. Guillemin V and Pollack A 1974 Differential Topology (Englewood Cliffs, NJ: Prentice-Hall)
29. Haggman B C, Horndeski G W and Mess G 1980 Properties of a covering space defined by Hawking J. Math. Phys. 21 2412-6
30. Hawking S W and Ellis G F R 1973 The Large Scale Structure of Space-Time (Cambridge: Cambridge University Press)
31. Herzlich M 1998 The positive mass theorem for black holes revisited J. Geom. Phys. 26 97-111
32. Heusler M 1997 On the uniqueness of the Papapetrou-Majumdar metric Class. Quantum Grav. 14 L129-34
33. Hicks N J 1965 Notes on Differential Geometry (Van Nostrand Mathematical Studies vol 3) (London: Van Nostrand Reinhold)
34. Israel W 1967 Event horizons in static vacuum space-times Phys. Rev. 164 1776-9
35. Israel W 1968 Event horizons in static electrovac space-times Commun. Math. Phys. 8 245-60
36. Kay B S and Wald R M 1991 Theorems on the uniqueness and thermal properties of stationary, nonsingular. quasi-free states on space-times with a bifurcate horizon Phys. Rep. 207 49-136
37. Kennefick D and Ó Murchadha N 1995 Weakly decaying asymptotically flat static and stationary solutions to the Einstein equations Class. Quantum Grav. 12 149-58
38. Künzle H P 1971 On the spherical symmetry of a static perfect fluid Commun. Math. Phys. 20 85-100
39. Lindblom L 1980 Some properties of static general relativistic stellar models J. Math. Phys. 21 1455-9
40. Masood-ul-Alam AKM 1992 Uniqueness proof of static charged black holes revisited Class. Quantum Grav. 9 L53-5
41. Rácz I and Wald RM 1992 Extensions of spacetimes with Killing horizons Class. Quantum Grav. 9 2643-56
42. Rácz I and Wald R M 1996 Global extensions of spacetimes describing asymptotic final states of black holes Class. Quantum Grav. 13 539-52
43. Ruback P 1988 A new uniqueness theorem for charged black holes Class. Quantum Grav. 5 L155-9
44. Scott S M and Szekeres P 1986 The Curzon singularity. II: Global picture Gen. Rel. Grav. 18 571-83
45. Simon W 1992 Radiative Einstein-Maxwell spacetimes and 'no-hair' theorems Class. Quantum Grav. 9 241-56
46. Sudarsky D and Wald R M 1993 Extrema of mass, stationarity and staticity. and solutions to the Einstein-Yang-Mills equations Phys. Rev. D 46 1453-74
47. Vishveshwara C V 1968 Generalization of the 'Schwarzschild surface' to arbitrary static and stationary metrics J. Math. Phys. 9 1319-22
48. Wald R M 1984 General Relativity (Chicago, IL: University of Chicago Press)
49. Walker M 1970 Bloc diagrams and the extension of timelike two-surfaces J. Math. Phys. 11 2280-6
50. Weinstein G 1996 N-black hole stationary and axially symmetric solutions of the Einstein/Maxwell equations Commun. Part. Differ. Equ. 21 1389-430