Rotating black rings on Taub-NUT



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.


Black Holes Black Holes in String Theory Integrable Equations in Physics 


  1. [1]
    R. Emparan and H.S. Reall, A rotating black ring solution in five-dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    R.C. Myers and M. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  3. [3]
    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].MathSciNetADSGoogle Scholar
  4. [4]
    P. Figueras, A black ring with a rotating 2-sphere, JHEP 07 (2005) 039 [hep-th/0505244] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    A. Pomeransky and R. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [INSPIRE].
  6. [6]
    Y. Morisawa, S. Tomizawa and Y. Yasui, Boundary value problem for black rings, Phys. Rev. D 77 (2008) 064019 [arXiv:0710.4600] [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    Y. Chen, K. Hong and E. Teo, Unbalanced Pomeransky-Senkov black ring, Phys. Rev. D 84 (2011)084030 [arXiv:1108.1849] [INSPIRE].ADSGoogle Scholar
  8. [8]
    Y. Chen and E. Teo, Black holes on gravitational instantons, Nucl. Phys. B 850 (2011) 253 [arXiv:1011.6464] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    E. Newman, L. Tamubrino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  10. [10]
    S. Hawking, Gravitational instantons, Phys. Lett. A 60 (1977) 81 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    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].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    D. Gaiotto, A. Strominger and X. Yin, 5D black rings and 4D black holes, JHEP 02 (2006) 023 [hep-th/0504126] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].MathSciNetADSGoogle Scholar
  14. [14]
    D. Gaiotto, A. Strominger and X. Yin, New connections between 4D and 5D black holes, JHEP 02 (2006) 024 [hep-th/0503217] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    V. Belinski and E. Verdaguer, Gravitational solitons, Cambridge University Press, Cmabridge U.K. (2001).CrossRefMATHGoogle Scholar
  16. [16]
    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].MathSciNetADSGoogle Scholar
  17. [17]
    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].ADSCrossRefGoogle Scholar
  18. [18]
    S. Giusto and A. Saxena, Stationary axisymmetric solutions of five dimensional gravity, Class. Quant. Grav. 24 (2007) 4269 [arXiv:0705.4484] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  19. [19]
    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].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [INSPIRE].MathSciNetADSGoogle Scholar
  21. [21]
    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].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    D.J. Gross and M.J. Perry, Magnetic monopoles in Kaluza-Klein theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    R. Sorkin, Kaluza-Klein monopole, Phys. Rev. Lett. 51 (1983) 87 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    J.D. Jackson, Classical electrodynamics, John Wiley, U.S.A. (1999).MATHGoogle Scholar
  25. [25]
    H. Elvang and P. Figueras, Black Saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    H. Elvang and M.J. Rodriguez, Bicycling black rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    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].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70 (2004) 124002 [hep-th/0408141] [INSPIRE].MathSciNetADSGoogle Scholar
  29. [29]
    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].MathSciNetADSCrossRefMATHGoogle Scholar
  30. [30]
    R. Emparan, Rotating circular strings and infinite nonuniqueness of black rings, JHEP 03 (2004) 064 [hep-th/0402149] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    H. Ishihara and K. Matsuno, Kaluza-Klein black holes with squashed horizons, Prog. Theor. Phys. 116 (2006) 417 [hep-th/0510094] [INSPIRE].MathSciNetADSCrossRefMATHGoogle Scholar
  32. [32]
    T. Wang, A rotating Kaluza-Klein black hole with squashed horizons, Nucl. Phys. B 756 (2006) 86 [hep-th/0605048] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    G. Gibbons and D. Wiltshire, Black holes in Kaluza-Klein theory, Annals Phys. 167 (1986) 201 [Erratum ibid. 176 (1987) 393] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    D. Rasheed, The rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    P. Figueras and J. Lucietti, On the uniqueness of extremal vacuum black holes, Class. Quant. Grav. 27 (2010) 095001 [arXiv:0906.5565] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    S. Hollands, Horizon area-angular momentum inequality in higher dimensional spacetimes, Class. Quant. Grav. 29 (2012) 065006 [arXiv:1110.5814] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    H.S. Reall, Counting the microstates of a vacuum black ring, JHEP 05 (2008) 013 [arXiv:0712.3226] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    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].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    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].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Department of PhysicsNational University of SingaporeSingaporeSingapore
  2. 2.Centre for Gravitational Physics, College of Physical and Mathematical SciencesThe Australian National UniversityCanberraAustralia

Personalised recommendations