Skip to main content
SpringerLink
Log in

A scalar field condensation instability of rotating Anti-de Sitter black holes

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

Abstract

Near-extreme Reissner-Nordström-anti-de Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the Breitenlöhner-Freedman bound. It is shown that a similar instability afflicts near-extreme large rotating AdS black holes, and near-extreme hyperbolic Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole solutions are determined numerically. Some stability results for (possibly charged) scalar fields in black hole backgrounds are proved. For most of the extreme black holes we consider, these demonstrate stability if the “effective mass” respects the near-horizon BF bound. Small spherical Reissner-Nordström-AdS black holes are an interesting exception to this result.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].

    ADS  Google Scholar 

  2. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Ann. Phys. 144 (1982) 249 [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. P. Breitenlohner and D.Z. Freedman, Positive energy in Anti-de Sitter backgrounds and gauged extended supergravity, Phys. Lett. B 115 (1982) 197 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. L. Mezincescu and P.K. Townsend, Stability at a local maximum in higher dimensional Anti-de Sitter space and applications to supergravity, Ann. Phys. 160 (1985) 406 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  7. J. Sonner, A rotating holographic superconductor, Phys. Rev. D 80 (2009) 084031 [arXiv:0903.0627] [SPIRES].

    ADS  Google Scholar 

  8. S.W. Hawking, C.J. Hunter and M. Taylor, Rotation and the AdS/CFT correspondence, Phys. Rev. D 59 (1999) 064005 [hep-th/9811056] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [SPIRES].

    Article  ADS  Google Scholar 

  10. P. Basu et al., Small hairy black holes in global AdS spacetime, JHEP 10 (2010) 045 [arXiv:1003.3232] [SPIRES].

    Article  ADS  Google Scholar 

  11. S. Bhattacharyya, S. Minwalla and K. Papadodimas, Small hairy black holes in AdS 5 × S 5, arXiv:1005.1287 [SPIRES].

  12. G. Holzegel, On the massive wave equation on slowly rotating Kerr-AdS spacetimes, Commun. Math. Phys. 294 (2010) 169 [arXiv:0902.0973] [SPIRES].

    Article  MathSciNet  Google Scholar 

  13. T. Hertog, Towards a novel no-hair theorem for black holes, Phys. Rev. D 74 (2006) 084008 [gr-qc/0608075] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  14. H.K. Kunduri, J. Lucietti and H.S. Reall, Gravitational perturbations of higher dimensional rotating black holes: tensor perturbations, Phys. Rev. D 74 (2006) 084021 [hep-th/0606076] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. J.S.F. Chan and R.B. Mann, Scalar wave falloff in topological black hole backgrounds, Phys. Rev. D 59 (1999) 064025 [SPIRES].

    ADS  Google Scholar 

  18. R. Aros, C. Martinez, R. Troncoso and J. Zanelli, Quasinormal modes for massless topological black holes, Phys. Rev. D 67 (2003) 044014 [hep-th/0211024] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  19. W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical recipes in c++: the art of scientific computing, Cambridge University Press, Cmabridge U.K. (2002).

    Google Scholar 

  20. L.N. Trefethen, Spectral methods in MATLAB, SIAM, Philadelphia U.S.A. (2000).

    MATH  Google Scholar 

  21. A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. J. Fernandez-Gracia and B. Fiol, A no-hair theorem for extremal black branes, JHEP 11 (2009) 054 [arXiv:0906.2353] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The general Kerr-de Sitter metrics in all dimensions, J. Geom. Phys. 53 (2005) 49 [hep-th/0404008] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, Rotating black holes in higher dimensions with a cosmological constant, Phys. Rev. Lett. 93 (2004) 171102 [hep-th/0409155] [SPIRES].

    Article  ADS  Google Scholar 

  25. G.W. Gibbons, M.J. Perry and C.N. Pope, The first law of thermodynamics for Kerr-Anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. J.B. Gutowski and H.S. Reall, Supersymmetric AdS 5 black holes, JHEP 02 (2004) 006 [hep-th/0401042] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. R. Monteiro, M.J. Perry and J.E. Santos, Semiclassical instabilities of Kerr-AdS black holes, Phys. Rev. D 81 (2010) 024001 [arXiv:0905.2334] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  28. O.J.C. Dias, P. Figueras, R. Monteiro, J.E. Santos and R. Emparan, Instability and new phases of higher-dimensional rotating black holes, Phys. Rev. D 80 (2009) 111701 [arXiv:0907.2248] [SPIRES].

    ADS  Google Scholar 

  29. O.J.C. Dias, P. Figueras, R. Monteiro, H.S. Reall and J.E. Santos, An instability of higher-dimensional rotating black holes, JHEP 05 (2010) 076 [arXiv:1001.4527] [SPIRES].

    Article  ADS  Google Scholar 

  30. S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev. D 61 (2000) 024014 [hep-th/9908109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  31. V. Cardoso, O.J.C. Dias, J.P.S. Lemos and S. Yoshida, The black hole bomb and superradiant instabilities, Phys. Rev. D 70 (2004) 044039 [hep-th/0404096] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  32. V. Cardoso and O.J.C. Dias, Small Kerr-Anti-de Sitter black holes are unstable, Phys. Rev. D 70 (2004) 084011 [hep-th/0405006] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  33. V. Cardoso, O.J.C. Dias and S. Yoshida, Classical instability of Kerr-AdS black holes and the issue of final state, Phys. Rev. D 74 (2006) 044008 [hep-th/0607162] [SPIRES].

    ADS  Google Scholar 

  34. N. Uchikata, S. Yoshida and T. Futamase, Scalar perturbations of Kerr-AdS black holes, Phys. Rev. D 80 (2009) 084020 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  35. B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations, Commun. Math. Phys. 10 (1968) 280 [SPIRES].

    MATH  Google Scholar 

  36. K. Maeda, S. Fujii and J.-i. Koga, The final fate of instability of Reissner-Nordström-Anti-de Sitter black holes by charged complex scalar fields, Phys. Rev. D 81 (2010) 124020 [arXiv:1003.2689] [SPIRES].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.

    Óscar J. C. Dias, Ricardo Monteiro, Harvey S. Reall & Jorge E. Santos

  2. CFP, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 4169-007, Porto, Portugal

    Ricardo Monteiro & Jorge E. Santos

Authors
  1. Óscar J. C. Dias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Monteiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Harvey S. Reall
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jorge E. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Óscar J. C. Dias.

Additional information

ArXiv ePrint: 1007.3745

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dias, Ó.J.C., Monteiro, R., Reall, H.S. et al. A scalar field condensation instability of rotating Anti-de Sitter black holes. J. High Energ. Phys. 2010, 36 (2010). https://doi.org/10.1007/JHEP11(2010)036

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2010)036

Keywords

Search

Navigation