On the uniqueness of extremal vacuum black holes

Classical and Quantum Gravity

Volumn 27, Issue 9, 2010, Pages

  Figueras, Pau ^a   Lucietti, James ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77950580043     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/9/095001     Document Type: Article

References (67)

1. Carter B 1971 Axisymmetric black hole has only two degrees of freedom Phys. Rev. Lett. 26 331
2. Carter B 1973 Black hole equilibrium states: II General theory of stationary black hole states Black Holes: Proc. 1972 Les Houches Summer School ed B DeWitt and C DeWitt (New York: Gordon and Breach) pp 125-210
3. Robinson D C 1975 Uniqueness of the Kerr black hole Phys. Rev. Lett. 34 905
4. Mazur P O 1982 Proof of uniqueness of the Kerr-Newman black hole solution J. Phys. A: Math. Gen. 15 3173
5. Mazur P O 1984 Black hole uniqueness from a hidden symmetry of Einstein's gravity Gen. Rel. Grav. 16 211
6. Bunting G 1983 Proof of the uniqueness conjecture for black holes PhD Thesis Department of Mathematics, University of New England, Armidale, NSW, Australia
7. Carter B 1985 Bunting identity and Mazur identity for non-linear elliptic systems including the black hole equilibrium problem Commun. Math. Phys. 99 563
8. Chrusciel P T and Costa J L 2008 On uniqueness of stationary vacuum black holes arXiv:0806.0016 [gr-qc]
9. Hawking S W 1972 Black holes in general relativity Commun. Math. Phys. 25 152
10. Hawking S W and Ellis G F R 1973 The Large Scale Structure of Space-Time (Cambridge: Cambridge University Press)
11. Chrusciel P T and Wald R M 1994 On the topology of stationary black holes Class. Quantum. Grav. 11 L147 (arXiv:gr-qc/9410004)
12. Galloway G J, Schleich K, Witt D M and Woolgar E 1999 Topological censorship and higher genus black holes Phys. Rev. D 60 104039 (arXiv:gr-qc/9902061)
13. Sudarsky D and Wald R M 1992 Extrema of mass, stationarity, and staticity, and solutions to the Einstein Yang-Mills equations Phys. Rev. D 46 1453
14. Israel W 1967 Event horizons in static vacuum space-times Phys. Rev. 164 1776
15. Bunting G L and Masood-ul-Alam A K M 1987 Nonexistence of multiple black holes in asymptotically Euclidean static vacuum space-times Gen. Rel. Grav. 19 147-54
16. Chrusciel P T 1997 On rigidity of analytic black holes Commun. Math. Phys. 189 1 (arXiv:gr-qc/9610011)
17. Friedrich H, Racz I and Wald R M 1999 On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon Commun. Math. Phys. 204 691 (arXiv:gr-qc/9811021)
18. Ernst F J 1968 New formulation of the axially symmetric gravitational field problem Phys. Rev. 167 1175
19. Mazur P O 1983 A relationship between the electrovacuum Ernst equations and nonlinear sigma model Acta Phys. Polon. B 14 219
20. Chrusciel P T, Reall H S and Tod P 2006 On non-existence of static vacuum black holes with degenerate components of the event horizon Class. Quantum. Grav. 23 549 (arXiv:gr-qc/0512041) (Pubitemid 43240837)
21. Hollands S and Ishibashi A 2008 On the 'Stationary implies axisymmetric' theorem for extremal black holes in higher dimensions arXiv:0809.2659 [gr-qc]
22. Kunduri H K, Lucietti J and Reall H S 2007 Near-horizon symmetries of extremal black holes Class. Quantum. Grav. 24 4169 (arXiv:0705.4214 [hep-th])
23. Hajicek P 1974 Three remarks on axisymmetric stationary horizons Commun. Math. Phys. 36 305-20
24. Lewandowski J and Pawlowski T 2003 Extremal isolated horizons: a local uniqueness theorem Class. Quantum. Grav. 20 587 (arXiv:gr-qc/0208032) (Pubitemid 36508124)
25. Kunduri H K and Lucietti J 2008 A classification of near-horizon geometries of extremal vacuum black holes arXiv:0806.2051 [hep-th]
26. Myers R C and Perry M J 1986 Black holes in higher dimensional space-times Ann. Phys. 172 304
27. Emparan R and Reall H S 2002 Generalized Weyl solutions Phys. Rev. D 65 084025 (arXiv:hep-th/0110258)
28. Emparan R and Reall H S 2002 A rotating black ring in five dimensions Phys. Rev. Lett. 88 101101 (arXiv:hep-th/0110260) (Pubitemid 34435468)
29. Pomeransky A A and Sen'kov R A 2006 Black ring with two angular momenta arXiv:hep-th/0612005
30. Galloway G J and Schoen R 2006 A generalization of Hawking's black hole topology theorem to higher dimensions Commun. Math. Phys. 266 571 (arXiv:gr-qc/0509107) (Pubitemid 44091007)
31. Galloway G J 2006 Rigidity of outer horizons and the topology of black holes arXiv:gr-qc/0608118
32. Gibbons G W, Ida D and Shiromizu T 2003 Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions Prog. Theor. Phys. Suppl. 148 284 (arXiv:gr-qc/0203004) (Pubitemid 36543632)
33. Rogatko M 2005 Staticity theorem for higher dimensional generalized Einstein-Maxwell system Phys. Rev. D 71 024031 (arXiv:hep-th/0501216) (Pubitemid 44966587)
34. Hollands S, Ishibashi A and Wald R M 2007 A higher dimensional stationary rotating black hole must be axisymmetric Commun. Math. Phys. 271 699 (arXiv:gr-qc/0605106)
35. Moncrief V and Isenberg J 2008 Symmetries of higher dimensional black holes Class. Quantum. Grav. 25 195015 (arXiv:0805.1451 [gr-qc])
36. Harmark T 2004 Stationary and axisymmetric solutions of higher-dimensional general relativity Phys. Rev. D 70 124002 (arXiv:hep-th/0408141) (Pubitemid 44643346)
37. Chrusciel P T 2008 On higher dimensional black holes with Abelian isometry group arXiv:0812.3424 [gr-qc]
38. Hollands S and Yazadjiev S 2008 Uniqueness theorem for 5-dimensional black holes with two axial Killing fields Commun. Math. Phys. 283 749 (arXiv:0707.2775 [gr-qc])
39. Hollands S and Yazadjiev S 2008 A uniqueness theorem for stationary Kaluza-Klein black holes arXiv:0812.3036 [gr-qc]
40. Gowdy R H 1974 Vacuum space-times with two parameter spacelike isometry groups and compact invariant hypersurfaces: topologies and boundary conditions Ann. Phys. 83 203
41. Chrusciel P 1990 On space-times with U(1) × U(1) symmetric compact Cauchy surfaces Ann. Phys. 202 100
42. Evslin J 2008 Geometric engineering 5d black holes with rod diagrams J. High Energy Phys. JHEP09(2008)004 (arXiv:0806.3389 [hep-th])
43. Chen Y and Teo E 2008 A rotating black lens solution in five dimensions Phys. Rev. D 78 064062 (arXiv:0808.0587 [gr-qc])
44. Weinstein G 1990 On rotating black holes in equilibrium in general relativity Commun. Pure Appl. Math. 43 903
45. Weinstein G 1995 On the Dirichlet problem for harmonic maps with prescribed singularities Duke Math. J. 77 135-65 (Pubitemid 126344876)
46. Chrusciel P T, Li Y and Weinstein G 2008 Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum Ann. Phys. 323 2591 (arXiv:0712.4064 [gr-qc])
47. Zaslavsky O B 1998 Horizon/matter systems near the extreme state Class. Quantum. Grav. 15 3251 (arXiv:gr-qc/9712007)
48. Bardeen J M and Horowitz G T 1999 The extreme Kerr throat geometry: a vacuum analog of AdS(2) × S(2) Phys. Rev. D 60 104030 (arXiv:hep-th/ 9905099)
49. Figueras P, Kunduri H K, Lucietti J and Rangamani M 2008 Extremal vacuum black holes in higher dimensions Phys. Rev. D 78 044042 (arXiv:0803.2998 [hep-th])
50. Camps J, Emparan R, Figueras P, Giusto S and Saxena A 2009 Black rings in Taub-NUT and D0-D6 interactions J. High Energy Phys. JHEP02(2009)021 (arXiv:0811.2088 [hep-th])
51. Elvang H and Figueras P 2007 Black saturn J. High Energy Phys. JHEP05(2007)050 (arXiv:hep-th/0701035)
52. Iguchi H and Mishima T 2007 Black di-ring and infinite nonuniqueness Phys. Rev. D 75 064018 (arXiv:hep-th/0701043)
53. Iguchi H and Mishima T 2008 Phys. Rev. D 78 069903 (Erratum)
54. Evslin J and Krishnan C 2009 Class. Quantum. Grav. 26 125018 (arXiv:0706.1231 [hep-th])
55. Izumi K 2008 Orthogonal black di-ring solution Prog. Theor. Phys. 119 757 (arXiv:0712.0902 [hep-th])
56. Elvang H and Rodriguez M J 2008 Bicycling black rings J. High Energy Phys. JHEP04(2008)045 (arXiv:0712.2425 [hep-th])
57. 2 generating technique for minimal D = 5 supergravity and black rings Phys. Rev. D 76 104032 (arXiv:0708.2361 [hep-th])
58. Bouchareb A, Clement G, Chen C M, Gal'tsov D V, Scherbluk N G and Wolf T 2008 Phys. Rev. D 78 029901 (Erratum)
59. 35D supergravity Phys. Rev. D 78 064033 (arXiv:0805.3924 [hep-th])
60. Tomizawa S, Yasui Y and Ishibashi A 2009 A uniqueness theorem for charged rotating black holes in five-dimensional minimal supergravity arXiv:0901.4724 [hep-th]
61. Hollands S and Yazadjiev S 2008 A uniqueness theorem for 5-dimensional Einstein-Maxwell black holes Class. Quantum. Grav. 25 095010 (arXiv:0711.1722 [gr-qc])
62. Kunduri H K and Lucietti J 2009 Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes Class. Quantum. Grav. 26 055019 (arXiv:0812.1576 [hep-th])
63. Reall H S 2003 Higher dimensional black holes and supersymmetry Phys. Rev. D 68 024024 (arXiv:hep-th/0211290)
64. Reall H S 2004 Phys. Rev. D 70 089902 (Erratum)
65. Kunduri H K and Lucietti J 2009 Static near-horizon geometries in five dimensions arXiv:0907.0410 [hep-th]
66. Amsel A J, Horowitz G T, Marolf D and Roberts M M 2009 Uniqueness of extremal Kerr and Kerr-Newman black holes arXiv:0906.2367 [gr-qc]
67. Meinel R, Ansorg M, Kleinwachter A, Neugebauer G and Petroff D 2008 Relativistic Figures of Equilibrium (Cambridge: Cambridge University Press) (section 2.4)