- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Vacuum energy in Kerr-AdS black holes

Gonzalo Olavarria*

Rodrigo Olea†

  • Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile

  • Departamento de Ciencias Físicas, Universidad Andres Bello, República 220, Santiago, Chile

  • *gonzalo.olavarria.u@mail.pucv.cl
  • †rodrigo.olea@unab.cl
PDF

Phys. Rev. D 89, 026001 – Published 9 January, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.026001

Abstract

We compute the vacuum energy for Kerr black holes with anti–de Sitter (AdS) asymptotics in dimensions 5≤D≤9 with all rotation parameters. The calculations are carried out employing an alternative regularization scheme for asymptotically AdS gravity, which considers supplementing the bulk action with counterterms which are a given polynomial in the extrinsic and intrinsic curvatures of the boundary (also known as Kounterterms). The Kerr-Schild form of the rotating solutions enables us to identify the vacuum energy as coming from the part of the metric that corresponds to a global AdS spacetime written in oblate spheroidal coordinates. We find that the zero-point energy for higher-dimensional Kerr-AdS reduces to one of a Schwarzschild-AdS black hole when all the rotation parameters are equal to each other, a fact that is well known in five dimensions. We also sketch a compact expression for the vacuum energy formula in terms of asymptotic quantities that might be useful to extend the computations to higher odd dimensions.

View figure in article

Article Text

References (47)

  1. J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998); Int. J. Theor. Phys. 38, 1113 (1999).
  2. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998).
  3. E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
  4. S. W. Hawking, C. J. Hunter, and M. Taylor, Phys. Rev. D 59, 064005 (1999).
  5. A. M. Awad and C. V. Johnson, Phys. Rev. D 61, 084025 (2000).
  6. S. Das and R. B. Mann, J. High Energy Phys. 08 (2000) 033.
  7. A. M. Awad and C. V. Johnson, Phys. Rev. D 63, 124023 (2001).
  8. R.-G. Cai, L.-M. Cao, and D.-W. Pang, Phys. Rev. D 72, 044009 (2005).
  9. I. Papadimitriou and K. Skenderis, J. High Energy Phys. 08 (2005) 004.
  10. G. W. Gibbons, M. J. Perry, and C. N. Pope, Phys. Rev. Lett. 95, 231601 (2005).
  11. A. M. Awad, Int. J. Mod. Phys. D 18, 405 (2009).
  12. M. Giammatteo and I. G. Moss, Classical Quantum Gravity 22, 1803 (2005).
  13. O. J. C. Dias and J. E. Santos, J. High Energy Phys. 10 (2013) 156.
  14. S. W. Hawking and D. N. Page, Commun. Math. Phys. 87, 577 (1983).
  15. K. Murata, T. Nishioka, N. Tanahashi, and H. Yumisaki, Prog. Theor. Phys. 120, 473 (2008).
  16. Y.-D. Tsai, X. N. Wu, and Y. Yang, Phys. Rev. D 85, 044005 (2012).
  17. J. Sonner, Phys. Rev. D 80, 084031 (2009).
  18. S. Bhattacharyya, S. Lahiri, R. Loganayagam, and S. Minwalla, J. High Energy Phys. 09 (2008) 054.
  19. M. M. Caldarelli, O. J. C. Dias, R. Emparan, and D. Klemm, J. High Energy Phys. 04 (2009) 024.
  20. R. Monteiro, M. J. Perry, and J. E. Santos, Phys. Rev. D 80, 024041 (2009).
  21. R. Monteiro, M. J. Perry, and J. E. Santos, Phys. Rev. D 81, 024001 (2010).
  22. O. J. C. Dias, P. Figueras, R. Monteiro, J. E. Santos, and R. Emparan, Phys. Rev. D 80, 111701 (2009).
  23. C. Fefferman and C. Graham, in Elie Cartan et les Mathématiques d’aujourd’hui (Astérisque, Paris, 1985), p. 95; C. Graham, arXiv:math/9909042; C. Graham and E. Witten, Nucl. Phys. B546 52 (1999).
  24. V. Balasubramanian and P. Kraus, Commun. Math. Phys. 208, 413 (1999).
  25. R. Emparan, C. V. Johnson, and R. C. Myers, Phys. Rev. D 60, 104001 (1999).
  26. G. T. Horowitz and R. C. Myers, Phys. Rev. D 59, 026005 (1998).
  27. M. C. N. Cheng and K. Skenderis, J. High Energy Phys. 08 (2005) 107.
  28. R. Olea, J. High Energy Phys. 04 (2007) 073.
  29. M. Henningson and K. Skenderis, J. High Energy Phys. 07 (1998) 023.
  30. S. de Haro, S. N. Solodukhin, and K. Skenderis, Commun. Math. Phys. 217, 595 (2001).
  31. K. Skenderis, Classical Quantum Gravity 19, 5849 (2002).
  32. G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).
  33. J. W. York, Jr., Phys. Rev. Lett. 28, 1082 (1972).
  34. R. Olea, J. High Energy Phys. 06 (2005) 023.
  35. O. Miskovic and R. Olea, Phys. Rev. D 79, 124020 (2009).
  36. R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).
  37. R. P. Kerr and A. Schild, Proc. Symp. Appl. Math. 17, 199 (1965).
  38. B. Carter, Commun. Math. Phys. 10, 280 (1968).
  39. R. C. Myers and M. J. Perry, Ann. Phys. (N.Y.) 172, 304 (1986).
  40. G. W. Gibbons, H. Lu, D. N. Page, and C. N. Pope, J. Geom. Phys. 53, 49 (2005).
  41. G. W. Gibbons, M. J. Perry, and C. N. Pope, Classical Quantum Gravity 22, 1503 (2005).
  42. Conserved charges of higher-dimensional Kerr-AdS spacetimes were computed, e.g., in S. Deser, I. Kanik, and B. Tekin, Classical Quantum Gravity 22, 3383 (2005).
  43. A. Ashtekar and A. Magnon, Classical Quantum Gravity 1, L39 (1984).
  44. A. Ashtekar and S. Das, Classical Quantum Gravity 17, L17 (2000).

  45. The results contained in Sec. V were obtained using GRTensorII for Maple. For a reference to the package, the reader may consult http://grtensor.org.

  46. The Casimir energy for the seven-dimensional rotating black hole was obtained in Ref. [10] using a coordinate system for Kerr-AdS that leaves the asymptotic region static. As a consequence, the vacuum energy does not depend on the rotation parameters and it coincides with the vale for the Schwarzschild black hole.

  47. O. Miskovic, G. Olavarria, and R. Olea (work in progress).

Outline

Information

Phys. Rev. D 89, 026001– Published 9 January, 2014
  • Received 22 August 2013

© 2014 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation