Abstract
We present numerical evidence for the existence of several types of static black hole solutions with a nonspherical event horizon topology in d ≥ 6 spacetime dimensions. These asymptotically flat configurations are found for a specific metric ansatz and can be viewed as higher dimensional counterparts of the d = 5 static black rings, dirings and black Saturn. Similar to that case, they are supported against collapse by conical singularities. The issue of rotating generalizations of these solutions is also considered.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Emparan and H.S. Reall, A rotating black ring in five dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [SPIRES].
R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [SPIRES].
R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Ann. Phys. 172 (1986) 304 [SPIRES].
H. Elvang and P. Figueras, Black Saturn, JHEP 05 (2007) 050 [hep-th/0701035] [SPIRES].
H. Iguchi and T. Mishima, Black di-ring and infinite nonuniqueness, Phys. Rev. D 75 (2007) 064018 [hep-th/0701043] [SPIRES].
J. Evslin and C. Krishnan, The black di-ring: an inverse scattering construction, Class. Quant. Grav. 26 (2009) 125018 [arXiv:0706.1231] [SPIRES].
H. Elvang and M.J. Rodriguez, Bicycling black rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [SPIRES].
M.J. Rodriguez, On the black hole species (by means of natural selection), arXiv:1003.2411 [SPIRES].
R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The phase structure of higher-dimensional black rings and black holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [SPIRES].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, New horizons for black holes and branes, JHEP 04 (2010) 046 [arXiv:0912.2352] [SPIRES].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [SPIRES].
D. Astefanesei, M.J. Rodriguez and S. Theisen, Thermodynamic instability of doubly spinning black objects, JHEP 08 (2010) 046 [arXiv:1003.2421] [SPIRES].
B. Kleihaus, J. Kunz and E. Radu, d ≥ 5 static black holes with S 2 × S d−4 event horizon topology, Phys. Lett. B 678 (2009) 301 [arXiv:0904.2723] [SPIRES].
G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [SPIRES].
T. Wiseman, Static axisymmetric vacuum solutions and non-uniform black strings, Class. Quant. Grav. 20 (2003) 1137 [hep-th/0209051] [SPIRES].
G.J. Galloway and R. Schoen, A generalization of Hawking’s black hole topology theorem to higher dimensions, Commun. Math. Phys. 266 (2006) 571 [gr-qc/0509107] [SPIRES].
S. Hollands, A. Ishibashi and R.M. Wald, A higher dimensional stationary rotating black hole must be axisymmetric, Commun. Math. Phys. 271 (2007) 699 [gr-qc/0605106] [SPIRES].
T. Harmark, Domain structure of black hole space-times, Phys. Rev. D 80 (2009) 024019 [arXiv:0904.4246] [SPIRES].
T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70 (2004) 124002 [hep-th/0408141] [SPIRES].
S. Hollands and S. Yazadjiev, Uniqueness theorem for 5-dimensional black holes with two axial Killing fields, Commun. Math. Phys. 283 (2008) 749 [arXiv:0707.2775] [SPIRES].
H. Kudoh, Doubly spinning black rings, Phys. Rev. D 75 (2007) 064006 [gr-qc/0611136] [SPIRES].
C. Herdeiro, B. Kleihaus, J. Kunz and E. Radu, On the Bekenstein-Hawking area law for black objects with conical singularities, Phys. Rev. D 81 (2010) 064013 [arXiv:0912.3386] [SPIRES].
D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [SPIRES].
C. Herdeiro, E. Radu and C. Rebelo, Thermodynamical description of stationary, asymptotically flat solutions with conical singularities, Phys. Rev. D 81 (2010) 104031 [arXiv:1004.3959] [SPIRES].
T. Regge, General relativity without coordinates, Nuovo Cim. 19 (1961) 558.
D. Astefanesei, M.J. Rodriguez and S. Theisen, Quasilocal equilibrium condition for black ring, JHEP 12 (2009) 040 [arXiv:0909.0008] [SPIRES].
B. Kleihaus, J. Kunz and E. Radu, New nonuniform black string solutions, JHEP 06 (2006) 016 [hep-th/0603119] [SPIRES].
E. Sorkin, Nonuniform black strings in various dimensions, Phys. Rev. D 74 (2006) 104027 [gr-qc/0608115] [SPIRES].
M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [SPIRES].
H. Kudoh and T. Wiseman, Properties of Kaluza-Klein black holes, Prog. Theor. Phys. 111 (2004) 475 [hep-th/0310104] [SPIRES].
H. Kudoh and T. Wiseman, Connecting black holes and black strings, Phys. Rev. Lett. 94 (2005) 161102 [hep-th/0409111] [SPIRES].
W. Schönauer and R. Weiß, Efficient vectorizable PDE solvers, J. Comput. Appl. Math. 27 (1989) 279.
M. Schauder, R. Weiß and W. Schönauer, The CA DSOL program package, Universität Karlsruhe, Interner Bericht Nr. 46/92 (1992).
B. Kleihaus and J. Kunz, Static axially symmetric Einstein Yang-Mills-dilaton solutions. I: regular solutions, Phys. Rev. D 57 (1998) 834 [gr-qc/9707045] [SPIRES].
B. Kleihaus and J. Kunz, Static axially symmetric Einstein-Yang-Mills-dilaton solutions. II: Black hole solutions, Phys. Rev. D 57 (1998) 6138 [gr-qc/9712086] [SPIRES].
R. Bach and H. Weyl, Neue Lösungen der Einsteinschen Gravitationsgleichungen B. Explizite Aufstellung statischer axialsymmetrischer Felder, Math. Zeit. 13 (1922) 134.
W. Israel and K.A. Khan, Collinear particles and Bondi dipoles in general relativity, Nuovo Cim. 33 (1964) 331.
H.S. Tan and E. Teo, Multi-black hole solutions in five dimensions, Phys. Rev. D 68 (2003) 044021 [hep-th/0306044] [SPIRES].
A.A. Pomeransky and R.A. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [SPIRES].
P. Figueras, A black ring with a rotating 2-sphere, JHEP 07 (2005) 039 [hep-th/0505244] [SPIRES].
T. Mishima and H. Iguchi, New axisymmetric stationary solutions of five-dimensional vacuum Einstein equations with asymptotic flatness, Phys. Rev. D 73 (2006) 044030 [hep-th/0504018] [SPIRES].
J. Kunz, F. Navarro-Lerida and J. Viebahn, Charged rotating black holes in odd dimensions, Phys. Lett. B 639 (2006) 362 [hep-th/0605075] [SPIRES].
H.K. Kunduri and J. Lucietti, Electrically charged dilatonic black rings, Phys. Lett. B 609 (2005) 143 [hep-th/0412153] [SPIRES].
S.S. Yazadjiev, Asymptotically and non-asymptotically flat static black rings in charged dilaton gravity, hep-th/0507097 [SPIRES].
B. Kleihaus, J. Kunz and E. Radu, Generalized Weyl solutions in D = 5 Einstein-Gauss-Bonnet theory: the static black ring, JHEP 02 (2010) 092 [arXiv:0912.1725] [SPIRES].
F. Schwartz, Existence of outermost apparent horizons with product of spheres topology, Commun. Anal. Geom. 16 (2008) 799 [arXiv:0704.2403] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1010.2898
Rights and permissions
About this article
Cite this article
Kleihaus, B., Kunz, J., Radu, E. et al. New generalized nonspherical black hole solutions. J. High Energ. Phys. 2011, 58 (2011). https://doi.org/10.1007/JHEP02(2011)058
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2011)058