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Quasinormal modes of dilaton-de Sitter black holes: scalar perturbations

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Abstract

Dilaton black hole solutions in low energy string theory (well known as GMGHS black holes) have analogue black holes with a cosmological constant derived by Gao and Zhang. Here, we study quasi normal modes of this dilaton-de Sitter black hole under neutral scalar field perturbations. We have employed the sixth order WKB analysis to compute the quasi normal mode frequencies. A detailed study is done for the quasi normal mode frequencies by varying the parameters in the theory such as the mass, cosmological constant, dilaton charge and the spherical harmonic index. For the massive scalar field we observed that the usual quasi resonance modes that exists for asymptotically flat black holes do not exist for this particular black hole. We have approximated the scalar field potential of the near-extreme dilaton de Sitter black hole with the Pöschl-Teller potential and have presented exact quasi normal frequencies.

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References

  1. Perlmutter, S., et al.: Measurements of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  2. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 1009 (1998); BVRI light curves for 22 type Ia supernovae. Astron. J. 117, 707 (1999)

    Article  ADS  Google Scholar 

  3. Spergel, D.N., et al.: (WMAP Collaboration), Wilkinson microwave anisotropy probe (WMAP) three year results: implications for cosmology. Astrophys. J. Suppl. 170, 377 (2007)

    Article  ADS  Google Scholar 

  4. Tegmark, M., et al.: (SDSS collaboration) cosmological parameters from SDSS and WMAP. Phys. Rev. D 69, 103501 (2004)

    Article  ADS  Google Scholar 

  5. Seljak, U., et al.: Cosmological parameter analysis including SDSS Ly\(\alpha \) forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy. Phys. Rev. D 71, 103515 (2005)

    Article  ADS  Google Scholar 

  6. Witten, E.: Quantum gravity in de Sitter space. arXiv:hep-th/0106109

  7. Dasguptha, K., Gwyn, R., McDonough, E., Mia, M., Tatar, R.: de Sitter vacua in type II B string theory: classical solutions and quantum corrections. JHEP 054, 1407 (2014)

    Google Scholar 

  8. Danielsson, U.H., Haque, S.S., Shiu, G., van Riet, T.: Towards classical de Sitter solutions in string theory. JHEP 0909, 114 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  9. Gibbons, G.W., Maeda, K.: Black holes and membranes in higher dimensional theories with dilaton fields. Nuclear Phys. B 298, 741 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  10. Garfinkle, D., Horowitz, G.T., Strominger, A.: Charged black holes in string theory. Phys. Rev. D 43, 3140 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  11. Poletti, S.J., Wiltshire, D.L.: Global properties of static spherically symmetric charged dilaton spacetimes with a Liouville potential. Phys. Rev. D 50, 7260 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  12. Gao, C.J., Zhang, S.N.: Dilaton black holes in de Sitter or anti-de Sitter universe. Phys. Rev. D 70, 124019 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  13. Gates, S.J., Zwiebach, B.: Gauged N\(=\)4 supergravity theory with a new scalar potential. Phys. Lett. B 123, 200 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  14. Zwiebach, B.: The inequivalent gauges of SO(4) supergravities. Nuclear Phys. B 238, 367 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  15. Easther, R.: Exact superstring motivated cosmological models. Classic Quantum Gravity 10, 2203 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  16. Dehghani, M.H., Bazrafshan, A.: Asymptotically AdS magnetic branes in \((n+1)\) dimensional dilaton gravity. Can. J. Phys. 89, 1163 (2011)

    Article  ADS  Google Scholar 

  17. Sheykhi, A., Riazi, N., Mahzoon, M.H.: Asymptotically non-flat Einstein-Born-Infeld-dilaton black holes with Liouville-type potentials. Phy. Rev. D 74, 044025 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  18. Chan, K.C.K., Horne, J.H., Mann, R.B.: Charged dilaton black holes with unusual asymptotics. Nuclear Phys. B 447, 441 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Ferrari, V., Gualtieri, L.: Quasi-normal modes and gravitational wave astronomy. Gen. Relativ. Gravit. 40, 945 (2008)

    Article  ADS  MATH  Google Scholar 

  20. Morgan, J., Miranda, A.S., Zanchin, V.T.: Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence. JHEP 03, 169 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  21. Hod, S.: Bohr’s correspondence principle and the area spectrum of quantum black holes. Phys. Rev. Lett. 81, 4293 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Fernando, S.: Spinning dilaton black holes in 2+1 dimensions: quasinormal modes and the area spectrum. Phys. Rev. D 79, 124026 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. Kunstatter, G.: d-Dimensional black hole entropy spectrum from quasi-normal modes. Phys. Rev. Lett 90, 161301 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Konoplya, R.A., Zhidenko, A.: Quasinormal modes of black holes: from astrophysics to string theory. Rev. Mod. Phys. 83, 793 (2011)

    Article  ADS  Google Scholar 

  25. Ferrari, V., Pauri, M., Piazza, F.: Quasi-normal modes of charged, dilaton black holes. Phy. Rev. D 63, 064009 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  26. Fernando, S., Arnold, K.: Scalar perturbations of charged dilaton black holes. Gen. Relativ. Gravit. 36, 1805 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Konoplya, R.A.: Decay of charged scalar field around a black hole: quasinormal modes of R-N, R-N-AdS and dilaton black holes. Phys. Rev. D 66, 084007 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  28. Konoplya, R.A.: Quasinormal modes of the electrically charged dilaton black hole. Gen. Rewl. 34, 329 (2002)

    MathSciNet  MATH  Google Scholar 

  29. Shu, F., Shen, Y.: Quasinormal modes of charged black holes in string theory. Phys. Rev. D 70, 084046 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  30. Kokkotas, K.D., Konoplya, R.A., Zhidenko, A.: Bifurcation of the quasinormal spectrum of zero damped modes for rotating dilatonic black holes. arXiv:1507.05649

  31. Iyer, S., Will, C.M.: Black-hole normal modes: a WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering. Phys. Rev. D 35, 3621 (1987)

    Article  ADS  Google Scholar 

  32. Konoplya, R.A.: Quasinormal behavior of the D-dimensional Schwarzschild black hole and higher order WKB approach. Phys. Rev. D 68, 024018 (2003)

    Article  ADS  Google Scholar 

  33. Fernando, S.: Decay of massless Dirac field around the Born-Infeld black hole. Int. J. Mod. Phys. A 25, 669 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Fernando, S., Correa, J.: Quasi-normal modes of the Bardeen black hole: scalar perturbations. Phys. Rev. D 86, 64039 (2012)

    Article  ADS  Google Scholar 

  35. Fernando, S., Clark, T.: Black holes in massive gravity: quasinormal modes of scalar perturbations. Gen. Relativ. Gravit. 46, 1834 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Horowitz, G.T., Hubeny, V.E.: Quasinormal modes of AdS black holes and the approach to thermal equilibrium. Phys. Rev. D 62, 024027 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  37. Brady, P.R., Chambers, C.M., Krivan, W., Laguna, P.: Telling tails in the presence of a cosmological constant. Phys. Rev. D 55, 7538 (1997)

    Article  ADS  Google Scholar 

  38. Fernando, S.: Regular black holes in de Sitter universe: scalar field perturbations and quasinormal modes, to appear in Int. J. Mod. Phys. D. arXiv:1508.03581

  39. Gundlach, C., Price, R.H., Pullin, J.: Late-time behavior of stellar collapse and explosions: I linearized perturbations. Phys. Rev. D 49, 883 (1994)

    Article  ADS  Google Scholar 

  40. Bronnikov, K.A., Konoplya, R.A., Zhidenko, A.: Instabilities of wormholes and regular black holes supported by a phantom scalar field. Phy. Rev. D 86, 024028 (2012)

    Article  ADS  Google Scholar 

  41. Konoplya, R.A., Zhidenko, A.V.: Decay of massive scalar field in a Schwarzschild background. Phys. Lett. B 609, 377 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Ohashi, A., Sakagami, M.: Massive quasi-normal modes. Classic Quantum Gravity 21, 3973 (2004)

    Article  ADS  MATH  Google Scholar 

  43. Chang, J., Huang, J., Shen, Y.: Quasi-resonent modes of massive scalar fields in Schwarzschild–de Sitter space-time. Int. J. Theor. Phys. 46, 2617 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  44. Podolsky, J.: The structure of the extreme Schwarzschild–de Sitter space-time. Gen. Relativ. Gravit. 31, 1703 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. Fernando, S.: Cold, ultracold and Nariai black holes with quintessence. Gen. Relativ. Gravit. 45, 2053 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. Fernando, S.: Nariai black holes with quintessence. Mod. Phys. Lett. A 28, 13550189 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  47. Fernando, S.: Born-Infeld-de Sitter gravity: cold, ultracold and Nariai black holes. Int. J. Mod. Phys. D 22, 1350080 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Matyjasek, J., Sadurski, P., Tryniecki, D.: Inside the degenerate horizons of the regular black holes. Phys. Rev. D 87, 124025 (2013)

    Article  ADS  Google Scholar 

  49. Ferrari, V., Mashhoon, B.: New approach to the quasinormal modes of a black hole. Phys. Rev. D 30, 295 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  50. Cardoso, V., Lemos, J.P.S.: Quasinormal modes of the near extremal Schwarzschild–de Sitter black hole. Phys. Rev. D 67, 084020 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  51. Molina, C.: Quasinormal modes of d-dimensional spherical black holes with a near extreme cosmological constant. Phys. Rev. D 68, 064007 (2003)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgments

The author wish to thank R. A. Konoplya for providing the Mathematica file for WKB approximation.

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  1. Department of Physics and Geology, Northern Kentucky University, Highland Heights, KY, 41099, USA

    Sharmanthie Fernando

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  1. Sharmanthie Fernando
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Correspondence to Sharmanthie Fernando.

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Fernando, S. Quasinormal modes of dilaton-de Sitter black holes: scalar perturbations. Gen Relativ Gravit 48, 24 (2016). https://doi.org/10.1007/s10714-016-2020-y

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