Advertisement

Quasinormal modes, stability analysis and absorption cross section for 4-dimensional topological Lifshitz black hole

  • P. A. GonzálezEmail author
  • Felipe Moncada
  • Yerko Vásquez
Regular Article - Theoretical Physics

Abstract

We study scalar perturbations in the background of a topological Lifshitz black hole in four dimensions. We compute analytically the quasinormal modes and from these modes we show that topological Lifshitz black hole is stable. On the other hand, we compute the reflection and transmission coefficients and the absorption cross section and we show that there is a range of modes with high angular momentum which contributes to the absorption cross section in the low frequency limit. Furthermore, in this limit, we show that the absorption cross section decreases if the scalar field mass increases, for a real scalar field mass.

Keywords

Black Hole Scalar Field Transmission Coefficient Absorption Cross Section Neumann Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Y.V. is supported by FONDECYT grant 11121148, and by Dirección de Investigación y Desarrollo, Universidad de la Frontera, DIUFRO DI11-0071. P.G. acknowledges the hospitality of the Physics Department of Universidad de La Frontera where part of this work was made.

References

  1. 1.
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics. Class. Quantum Gravity 26, 224002 (2009). arXiv:0903.3246 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    R.B. Mann, Lifshitz topological black holes. J. High Energy Phys. 0906, 075 (2009). arXiv:0905.1136 [hep-th] ADSCrossRefGoogle Scholar
  3. 3.
    T. Regge, J.A. Wheeler, Stability of a Schwarzschild singularity. Phys. Rev. 108, 1063 (1957) MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    F.J. Zerilli, Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics. Phys. Rev. D 2, 2141 (1970) MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    F.J. Zerilli, Effective potential for even parity Regge–Wheeler gravitational perturbation equations. Phys. Rev. Lett. 24, 737 (1970) ADSCrossRefGoogle Scholar
  6. 6.
    K.D. Kokkotas, B.G. Schmidt, Quasi-normal modes of stars and black holes. Living Rev. Relativ. 2, 2 (1999). arXiv:gr-qc/9909058 MathSciNetADSGoogle Scholar
  7. 7.
    H.P. Nollert, Topical review: quasinormal modes: the characteristic ‘sound’ of black holes and neutron stars. Class. Quantum Gravity 16, R159 (1999) MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    E. Berti, V. Cardoso, A.O. Starinets, Quasinormal modes of black holes and black branes. Class. Quantum Gravity 26, 163001 (2009). arXiv:0905.2975 [gr-qc] MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    R.A. Konoplya, A. Zhidenko, Quasinormal modes of black holes: from astrophysics to string theory. Rev. Mod. Phys. 83, 793 (2011). arXiv:1102.4014 [gr-qc] ADSCrossRefGoogle Scholar
  10. 10.
    A.A. Starobinsky, S.M. Churilov, Sov. Phys. JETP 38, 1 (1974) ADSGoogle Scholar
  11. 11.
    G.W. Gibbons, Vacuum polarization and the spontaneous loss of charge by black holes. Commun. Math. Phys. 44, 245 (1975) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    D.N. Page, Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole. Phys. Rev. D 13, 198 (1976) ADSCrossRefGoogle Scholar
  13. 13.
    W.G. Unruh, Absorption cross-section of small black holes. Phys. Rev. D 14, 3251 (1976) ADSCrossRefGoogle Scholar
  14. 14.
    A. Dhar, G. Mandal, S.R. Wadia, Absorption versus decay of black holes in string theory and T symmetry. Phys. Lett. B 388, 51 (1996). hep-th/9605234 MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    B. Kol, A. Rajaraman, Fixed scalars and suppression of Hawking evaporation. Phys. Rev. D 56, 983 (1997). hep-th/9608126 MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    G.W. Gibbons, A.R. Steif, Anomalous fermion production in gravitational collapse. Phys. Lett. B 314, 13 (1993). gr-qc/9305018 MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    S. Hod, Bohr’s correspondence principle and the area spectrum of quantum black holes. Phys. Rev. Lett. 81, 4293 (1998). arXiv:gr-qc/9812002 MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    G. Kunstatter, D-dimensional black hole entropy spectrum from quasi-normal modes. Phys. Rev. Lett. 90, 161301 (2003). arXiv:gr-qc/0212014 MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    M. Maggiore, The physical interpretation of the spectrum of black hole quasinormal modes. Phys. Rev. Lett. 100, 141301 (2008). arXiv:0711.3145 [gr-qc] MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    G.T. Horowitz, V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium. Phys. Rev. D 62, 024027 (2000). arXiv:hep-th/9909056 MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)]. arXiv:hep-th/9711200 MathSciNetADSzbMATHGoogle Scholar
  22. 22.
    D. Birmingham, I. Sachs, S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes. Phys. Rev. Lett. 88, 151301 (2002). hep-th/0112055 MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    S. Kachru, X. Liu, M. Mulligan, Gravity duals of Lifshitz-like fixed points. Phys. Rev. D 78, 106005 (2008). arXiv:0808.1725 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    B. Cuadros-Melgar, J. de Oliveira, C.E. Pellicer, Stability analysis and area spectrum of 3-dimensional Lifshitz black holes. Phys. Rev. D 85, 024014 (2012). arXiv:1110.4856 [hep-th] ADSCrossRefGoogle Scholar
  25. 25.
    T. Moon, Y.S. Myung, Absorption cross section in Lifshitz black hole. arXiv:1205.2317 [hep-th]
  26. 26.
    S. Lepe, J. Lorca, F. Pena, Y. Vasquez, Scalar field scattering by a Lifshitz black hole under a non-minimal coupling. arXiv:1205.4460 [hep-th]
  27. 27.
    P.A. Gonzalez, J. Saavedra, Y. Vasquez, Quasinormal modes and stability analysis for 4-dimensional Lifshitz black hole. arXiv:1201.4521 [gr-qc]
  28. 28.
    A. Giacomini, G. Giribet, M. Leston, J. Oliva, S. Ray, Scalar field perturbations in asymptotically Lifshitz black holes. arXiv:1203.0582 [hep-th]
  29. 29.
    Y.S. Myung, T. Moon, Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes. arXiv:1204.2116 [hep-th]
  30. 30.
    M. Abramowitz, A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970) Google Scholar
  31. 31.
    P. Breitenlohner, D.Z. Freedman, Positive energy in anti-de Sitter backgrounds and gauged extended supergravity. Phys. Lett. B 115, 197 (1982) MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    P. Breitenlohner, D.Z. Freedman, Stability in gauged extended supergravity. Ann. Phys. 144, 249 (1982) MathSciNetADSzbMATHCrossRefGoogle Scholar
  33. 33.
    K.M. Case, Singular potentials. Phys. Rev. 80, 797 (1950) MathSciNetADSzbMATHCrossRefGoogle Scholar
  34. 34.
    D. Birmingham, I. Sachs, S. Sen, Three-dimensional black holes and string theory. Phys. Lett. B 413, 281 (1997). arXiv:hep-th/9707188 MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    W.T. Kim, J.J. Oh, Dilaton driven Hawking radiation in AdS(2) black hole. Phys. Lett. B 461, 189 (1999). arXiv:hep-th/9905007 MathSciNetADSzbMATHCrossRefGoogle Scholar
  36. 36.
    J.J. Oh, W. Kim, Absorption cross section in warped AdS3 black hole. J. High Energy Phys. 0901, 067 (2009). arXiv:0811.2632 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    H.C. Kao, W.Y. Wen, Absorption cross section in warped AdS3 black hole revisited. J. High Energy Phys. 0909, 102 (2009). arXiv:0907.5555 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    P. Gonzalez, C. Campuzano, E. Rojas, J. Saavedra, Greybody factors for topological massless black holes. J. High Energy Phys. 1006, 103 (2010). arXiv:1003.2753 [gr-qc] ADSGoogle Scholar
  39. 39.
    P. Gonzalez, E. Papantonopoulos, J. Saavedra, Chern–Simons black holes: scalar perturbations, mass and area spectrum and greybody factors. J. High Energy Phys. 1008, 050 (2010). arXiv:1003.1381 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  40. 40.
    S.R. Das, G.W. Gibbons, S.D. Mathur, Universality of low energy absorption cross sections for black holes. Phys. Rev. Lett. 78, 417 (1997). arXiv:hep-th/9609052 ADSCrossRefGoogle Scholar
  41. 41.
    S.W. Kim, W.T. Kim, J.J. Oh, Decay rate and low energy near horizon dynamics of acoustic black holes. Phys. Lett. B 608, 10 (2005). arXiv:gr-qc/0409003 ADSCrossRefGoogle Scholar
  42. 42.
    P.A. Gonzalez, J. Saavedra, Comments on absorption cross section for Chern–Simons black holes in five dimensions. Int. J. Mod. Phys. A 26, 3997 (2011). arXiv:1104.4795 [gr-qc] ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2012

Authors and Affiliations

  • P. A. González
    • 1
    • 2
    Email author
  • Felipe Moncada
    • 3
  • Yerko Vásquez
    • 3
  1. 1.Escuela de Ingeniería Civil en Obras Civiles, Facultad de Ciencias Físicas y MatemáticasUniversidad Central de ChileSantiagoChile
  2. 2.Universidad Diego PortalesSantiagoChile
  3. 3.Departamento de Ciencias Físicas, Facultad de Ingeniería, Ciencias y AdministraciónUniversidad de La FronteraTemucoChile

Personalised recommendations