Abstract
In this paper, we construct new solutions describing rotating black rings on Taub-NUT using the inverse-scattering method. These are five-dimensional vacuum spacetimes, generalising the Emparan-Reall and extremal Pomeransky-Sen’kov black rings to a Taub-NUT background space. When reduced to four dimensions in Kaluza-Klein theory, these solutions describe (possibly rotating) electrically charged black holes in superposition with a finitely separated magnetic monopole. Various properties of these solutions are studied, from both a five- and four-dimensional perspective.
Similar content being viewed by others
References
R. Emparan and H.S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].
R.C. Myers and M. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].
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] [INSPIRE].
P. Figueras, A black ring with a rotating 2-sphere, JHEP 07 (2005) 039 [hep-th/0505244] [INSPIRE].
A. Pomeransky and R. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [INSPIRE].
Y. Morisawa, S. Tomizawa and Y. Yasui, Boundary value problem for black rings, Phys. Rev. D 77 (2008) 064019 [arXiv:0710.4600] [INSPIRE].
Y. Chen, K. Hong and E. Teo, Unbalanced Pomeransky-Sen’kov black ring, Phys. Rev. D 84 (2011)084030 [arXiv:1108.1849] [INSPIRE].
Y. Chen and E. Teo, Black holes on gravitational instantons, Nucl. Phys. B 850 (2011) 253 [arXiv:1011.6464] [INSPIRE].
E. Newman, L. Tamubrino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].
S. Hawking, Gravitational instantons, Phys. Lett. A 60 (1977) 81 [INSPIRE].
H. Elvang, R. Emparan, D. Mateos and H.S. Reall, Supersymmetric 4D rotating black holes from 5D black rings, JHEP 08 (2005) 042 [hep-th/0504125] [INSPIRE].
D. Gaiotto, A. Strominger and X. Yin, 5D black rings and 4D black holes, JHEP 02 (2006) 023 [hep-th/0504126] [INSPIRE].
I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].
D. Gaiotto, A. Strominger and X. Yin, New connections between 4D and 5D black holes, JHEP 02 (2006) 024 [hep-th/0503217] [INSPIRE].
V. Belinski and E. Verdaguer, Gravitational solitons, Cambridge University Press, Cmabridge U.K. (2001).
A.A. Pomeransky, Complete integrability of higher-dimensional Einstein equations with additional symmetry and rotating black holes, Phys. Rev. D 73 (2006) 044004 [hep-th/0507250] [INSPIRE].
H. Iguchi, K. Izumi and T. Mishima, Systematic solution-generation of five-dimensional black holes, Prog. Theor. Phys. Suppl. 189 (2011) 93 [arXiv:1106.0387] [INSPIRE].
S. Giusto and A. Saxena, Stationary axisymmetric solutions of five dimensional gravity, Class. Quant. Grav. 24 (2007) 4269 [arXiv:0705.4484] [INSPIRE].
J. Ford, S. Giusto, A. Peet and A. Saxena, Reduction without reduction: adding KK-monopoles to five dimensional stationary axisymmetric solutions, Class. Quant. Grav. 25 (2008) 075014 [arXiv:0708.3823] [INSPIRE].
R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [INSPIRE].
J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [INSPIRE].
D.J. Gross and M.J. Perry, Magnetic monopoles in Kaluza-Klein theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].
R. Sorkin, Kaluza-Klein monopole, Phys. Rev. Lett. 51 (1983) 87 [INSPIRE].
J.D. Jackson, Classical electrodynamics, John Wiley, U.S.A. (1999).
H. Elvang and P. Figueras, Black Saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].
H. Elvang and M.J. Rodriguez, Bicycling black rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [INSPIRE].
Y. Chen and E. Teo, Rod-structure classification of gravitational instantons with U(1) × U(1) isometry, Nucl. Phys. B 838 (2010) 207 [arXiv:1004.2750] [INSPIRE].
T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70 (2004) 124002 [hep-th/0408141] [INSPIRE].
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] [INSPIRE].
R. Emparan, Rotating circular strings and infinite nonuniqueness of black rings, JHEP 03 (2004) 064 [hep-th/0402149] [INSPIRE].
H. Ishihara and K. Matsuno, Kaluza-Klein black holes with squashed horizons, Prog. Theor. Phys. 116 (2006) 417 [hep-th/0510094] [INSPIRE].
T. Wang, A rotating Kaluza-Klein black hole with squashed horizons, Nucl. Phys. B 756 (2006) 86 [hep-th/0605048] [INSPIRE].
G. Gibbons and D. Wiltshire, Black holes in Kaluza-Klein theory, Annals Phys. 167 (1986) 201 [Erratum ibid. 176 (1987) 393] [INSPIRE].
D. Rasheed, The rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [INSPIRE].
F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [INSPIRE].
P. Figueras and J. Lucietti, On the uniqueness of extremal vacuum black holes, Class. Quant. Grav. 27 (2010) 095001 [arXiv:0906.5565] [INSPIRE].
S. Hollands, Horizon area-angular momentum inequality in higher dimensional spacetimes, Class. Quant. Grav. 29 (2012) 065006 [arXiv:1110.5814] [INSPIRE].
H.S. Reall, Counting the microstates of a vacuum black ring, JHEP 05 (2008) 013 [arXiv:0712.3226] [INSPIRE].
I. Bena, G. Dall’Agata, S. Giusto, C. Ruef and N.P. Warner, Non-BPS black rings and black holes in Taub-NUT, JHEP 06 (2009) 015 [arXiv:0902.4526] [INSPIRE].
I. Bena, S. Giusto and C. Ruef, A black ring with two angular momenta in Taub-NUT, JHEP 06 (2011) 140 [arXiv:1104.0016] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1204.3116
Rights and permissions
About this article
Cite this article
Chen, Y., Teo, E. Rotating black rings on Taub-NUT. J. High Energ. Phys. 2012, 68 (2012). https://doi.org/10.1007/JHEP06(2012)068
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2012)068