Skip to main content
Log in

Rotating black rings on Taub-NUT

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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].

    Article  MathSciNet  ADS  Google Scholar 

  2. R.C. Myers and M. Perry, Black holes in higher dimensional space-times, Annals Phys. 172 (1986) 304 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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].

    MathSciNet  ADS  Google Scholar 

  4. P. Figueras, A black ring with a rotating 2-sphere, JHEP 07 (2005) 039 [hep-th/0505244] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Pomeransky and R. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [INSPIRE].

  6. Y. Morisawa, S. Tomizawa and Y. Yasui, Boundary value problem for black rings, Phys. Rev. D 77 (2008) 064019 [arXiv:0710.4600] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  7. Y. Chen, K. Hong and E. Teo, Unbalanced Pomeransky-Senkov black ring, Phys. Rev. D 84 (2011)084030 [arXiv:1108.1849] [INSPIRE].

    ADS  Google Scholar 

  8. Y. Chen and E. Teo, Black holes on gravitational instantons, Nucl. Phys. B 850 (2011) 253 [arXiv:1011.6464] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. E. Newman, L. Tamubrino and T. Unti, Empty space generalization of the Schwarzschild metric, J. Math. Phys. 4 (1963) 915 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  10. S. Hawking, Gravitational instantons, Phys. Lett. A 60 (1977) 81 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  12. D. Gaiotto, A. Strominger and X. Yin, 5D black rings and 4D black holes, JHEP 02 (2006) 023 [hep-th/0504126] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. D. Gaiotto, A. Strominger and X. Yin, New connections between 4D and 5D black holes, JHEP 02 (2006) 024 [hep-th/0503217] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. V. Belinski and E. Verdaguer, Gravitational solitons, Cambridge University Press, Cmabridge U.K. (2001).

    Book  MATH  Google Scholar 

  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].

    MathSciNet  ADS  Google Scholar 

  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].

    Article  ADS  Google Scholar 

  18. S. Giusto and A. Saxena, Stationary axisymmetric solutions of five dimensional gravity, Class. Quant. Grav. 24 (2007) 4269 [arXiv:0705.4484] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  20. R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  22. D.J. Gross and M.J. Perry, Magnetic monopoles in Kaluza-Klein theories, Nucl. Phys. B 226 (1983) 29 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. R. Sorkin, Kaluza-Klein monopole, Phys. Rev. Lett. 51 (1983) 87 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. J.D. Jackson, Classical electrodynamics, John Wiley, U.S.A. (1999).

    MATH  Google Scholar 

  25. H. Elvang and P. Figueras, Black Saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. H. Elvang and M.J. Rodriguez, Bicycling black rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  28. T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70 (2004) 124002 [hep-th/0408141] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. R. Emparan, Rotating circular strings and infinite nonuniqueness of black rings, JHEP 03 (2004) 064 [hep-th/0402149] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. H. Ishihara and K. Matsuno, Kaluza-Klein black holes with squashed horizons, Prog. Theor. Phys. 116 (2006) 417 [hep-th/0510094] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. T. Wang, A rotating Kaluza-Klein black hole with squashed horizons, Nucl. Phys. B 756 (2006) 86 [hep-th/0605048] [INSPIRE].

    Article  ADS  Google Scholar 

  33. G. Gibbons and D. Wiltshire, Black holes in Kaluza-Klein theory, Annals Phys. 167 (1986) 201 [Erratum ibid. 176 (1987) 393] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. D. Rasheed, The rotating dyonic black holes of Kaluza-Klein theory, Nucl. Phys. B 454 (1995) 379 [hep-th/9505038] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. F. Larsen, Rotating Kaluza-Klein black holes, Nucl. Phys. B 575 (2000) 211 [hep-th/9909102] [INSPIRE].

    Article  ADS  Google Scholar 

  36. P. Figueras and J. Lucietti, On the uniqueness of extremal vacuum black holes, Class. Quant. Grav. 27 (2010) 095001 [arXiv:0906.5565] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. S. Hollands, Horizon area-angular momentum inequality in higher dimensional spacetimes, Class. Quant. Grav. 29 (2012) 065006 [arXiv:1110.5814] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. H.S. Reall, Counting the microstates of a vacuum black ring, JHEP 05 (2008) 013 [arXiv:0712.3226] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Edward Teo.

Additional information

ArXiv ePrint: 1204.3116

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2012)068

Keywords

Navigation