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Quasinormal modes of Dirac field in Einstein–Born–Infeld dilaton black hole

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Abstract

The Dirac quasinormal modes of Einstein–Born–Infeld dilaton black holes are studied. We separate the Dirac equation in the curve spacetime into radial and angular parts by Newman–Penrose formalism, and we fortunately obtain the exact analytical solutions of these equations. Then we get the analytical expressions for the quasinormal modes of the black hole. Our results show that the quasinormal frequencies are purely imaginary which means the black hole is very stable. Furthermore, we find that the area spacing of the black hole is described by \(\Delta A_{min}=8\pi \hbar \) which supports Bekenstein’s conjecture.

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References

  1. Einstein, A.: Die Grundlage der allgemeinen Relativitätstheorie. Ann. Phys. 49, 769–822 (1916)

    Article  Google Scholar 

  2. Gibbons, G.W.: Vacuum polarization and the spontaneous loss of charge by black holes. Commun. Math. Phys. 44, 245 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  3. Schwarzschild, K.: Sitzungsber. Preuss. Akad.Wiss. Berlin.: On the gravitational field of a mass point according to Einstein’s theory. Math. Phys. 1916, 189 (1916)

    Google Scholar 

  4. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman, San Francisco (1973)

    Google Scholar 

  5. Frolov, V.P., Novikov, I.D.: Black Hole Physics: Basic Concepts and New Developments. Kluwer Academic, Dordrecht (1998)

    Book  Google Scholar 

  6. Vishveshwara, C.V.: Stability of the Schwarzschild metric. Phys. Rev. D 1, 2870 (1970)

    Article  ADS  Google Scholar 

  7. Vishveshwara, C.V.: Scattering of gravitational radiation by a Schwarzschild black-hole. Nature 227, 936 (1970)

    Article  ADS  Google Scholar 

  8. Abbott, B.P., et al.: [LIGO Scientific and Virgo Collaborations] Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116(6), 061102 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  9. Abbott, B.P., et al.: [LIGO Scientific and Virgo Collaborations] GW151226: observation of gravitational waves from a 22-Solar-Mass binary black hole coalescence. Phys. Rev. Lett. 116(24), 241103 (2016)

    Article  ADS  Google Scholar 

  10. Abbott, B.P., et al.: [LIGO Scientific and Virgo Collaborations] GW170104: observation of a 50-Solar-Mass binary black hole coalescence at redshift 0.2. Phys. Rev. Lett. 118(22), 221101 (2017)

    Article  ADS  Google Scholar 

  11. Lepe, S., Saavedra, J.: Quasinormal modes, superradiance and area spectrum for acoustic black holes. Phys. Lett. B 617, 174 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  12. Aros, R., Martinez, C., Troncoso, R., Zanelli, J.: Quasinormal modes for massless topological black holes. Phys. Rev. D 67, 044014 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  13. Jing, J.: Dirac quasinormal modes of Schwarzschild black hole. Phys. Rev. D 71, 124006 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  14. Jing, J., Pan, Q.: Dirac quasinormal frequencies of Schwarzschild-anti-de Sitter and Reissner–Nordström-anti-de Sitter black holes. Phys. Rev. D 71, 124011 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  15. Jing, J., Pan, Q.: Quasinormal modes and second order thermodynamic phase transition for Reissner–Nordström black hole. Phys. Lett. B 660, 13 (2008)

    Article  ADS  Google Scholar 

  16. Maggiore, M.: Physical interpretation of the spectrum of black hole quasinormal modes. Phys. Rev. Lett. 100, 141301 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  17. Chen, S., Jing, J.: Dynamical evolution of a scalar field coupling to Einstein’s tensor in the Reissner–Nordström black hole spacetime. Phys. Rev. D 82, 084006 (2010)

    Article  ADS  Google Scholar 

  18. Wang, B., Abdalla, E., Mann, R.B.: Scalar wave propagation in topological black hole backgrounds. Phys. Rev. D 65, 084006 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  19. 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  MathSciNet  Google Scholar 

  20. Wang, M., Herdeiro, C.: Maxwell perturbations on Kerr-anti-de Sitter black holes: quasinormal modes, superradiant instabilities, and vector clouds. Phys. Rev. D 93, 064066 (2016)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  22. Yao, W.P., Chen, S., Jing, J.: Quasinormal modes of a scalar perturbation coupling with Einstein’s tensor in the warped AdS3 black hole spacetime. Phys. Rev. D 83, 124018 (2011)

    Article  ADS  Google Scholar 

  23. Wang, M., Herdeiro, C., Jing, J.: Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: generic boundary conditions and new quasinormal modes. Phy. Rev. D 96, 104035 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  24. Xu, J.Y., Jing, J.: Dirac quasinormal modes and area spectrum of Horava–Lifshitz black holes. Ann. Phys. 389, 136 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  25. González, P.A., Papantonopoulos, E., Saavedra, J., Vásquez, Y.: Superradiant instability of near extremal and extremal four-dimensional charged hairy black holes in anti-de Sitter spacetime. Phys. Rev. D 95, 064046 (2017)

    Article  ADS  Google Scholar 

  26. Zangeneh, M.K., Wang, B., Sheykhi, A., Tang, Z.Y.: Charged scalar quasi-normal modes for linearly charged dilaton-Lifshitz solutions. Phys. Lett. B 771, 257–263 (2017)

    Article  ADS  Google Scholar 

  27. Hashemi, S.S., Zangeneh, M.K., Faizal, M.: Charged scalar quasi-normal modes for higher-dimensional Born-Infeld dilatonic black holes with Lifshitz scaling. arXiv:1901.11367

  28. Bekenstein, J.D.: The quantum mass spectrum of the Kerr black hole. Lett. Nuovo Cim. 11, 467 (1974)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  30. Kunstatter, G.: D-dimensional black hole entropy spectrum from quasi-normal modes. Phys. Rev. Lett. 90, 161301 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  31. Born, M.: On the quantum theory of the electromagnetic field. Proc. R. Soc. Lond. A 143(849), 410 (1934)

    Article  ADS  Google Scholar 

  32. Born, M., Infeld, L.: Foundations of the new field theory. Proc. R. Soc. Lond. A 144, 425 (1934)

    Article  ADS  Google Scholar 

  33. Johnson, C.V.: D-Branes. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  34. Zwiebach, B.: A First Course in String Theory. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  35. Leigh, R.G.: Dirac–Born–Infeld action from dirichlet \(\sigma \)-model. Mod. Phys. Lett. A 4, 2767 (1989)

    Article  ADS  Google Scholar 

  36. Tseytlin, A.A.: Vector field effective action in the open superstring theory. Nucl. Phys. B 276, 391 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  37. Jing, J., Chen, S.: Holographic superconductors in the Born–Infeld electrodynamics. Phys. Lett. B 686, 68 (2010)

    Article  ADS  Google Scholar 

  38. Jing, J., Wang, L., Pan, Q., Chen, S.: Holographic superconductors in Gauss–Bonnet gravity with Born–Infeld electrodynamics. Phys. Rev. D 83, 066010 (2011)

    Article  ADS  Google Scholar 

  39. Yao, W., Jing, J.: Analytical study on holographic superconductors for Born-Infeld electrodynamics in Gauss–Bonnet gravity with backreactions. JHEP 1305, 101 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  40. Yao, W., Jing, J.: Holographic entanglement entropy in insulator/superconductor transition with Born–Infeld electrodynamics. JHEP 1405, 058 (2014)

    Article  ADS  Google Scholar 

  41. Yao, W., Jing, J.: Holographic entanglement entropy in metal/superconductor phase transition with Born–Infeld electrodynamics. Nucl. Phys. B 889, 109 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  42. Wang, L., Jing, J.: General holographic superconductor models with Born–Infeld electrodynamics. Gen. Relativ. Gravit. 44, 1309 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  43. Yamazaki, R., Ida, D.: Black holes in three-dimensional Einstein–Born–Infeld-dilaton theory. Phys. Rev. D 64, 024009 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  44. Sheykhi, A., Riazi, N., Mahzoon, M.H.: Asymptotically nonflat Einstein–Born–Infeld-dilaton black holes with Liouville-type potential. Phys. Rev. D 74, 044025 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  45. Wiltshire, D.L.: Spherically symmetric solutions in dimensionally reduced spacetimes with a higher-dimensional cosmological constant. Phys. Rev. D 44, 1100 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  46. Mignemi, S., Wiltshire, D.L.: Black holes in higher-derivative gravity theories. Phys. Rev. D 46, 1475 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  47. Poletti, S.J., Wiltshire, D.L.: Erratum: Global properties of static spherically symmetric charged dilaton spacetimes with a Liouville potential [Phys. Rev. D 50, 7260 (1994)]. Phys. Rev. D 52, 3753 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  48. Clément, G., Gal’tsov, D., Leygnac, C.: Linear dilaton black holes. Phys. Rev. D 67, 024012 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  49. Cai, R., Wang, A.: Nonasymptotically AdS/dS solutions and their higher dimensional origins. Phys. Rev. D 70, 084042 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  50. Destounis, K., Panotopoulos, G., Rincón, Á.: Stability under scalar perturbations and quasinormal modes of 4D Einstein–Born–Infeld dilaton spacetime: exact spectrum. Eur. Phys. J. C 78(2), 139 (2018)

    Article  ADS  Google Scholar 

  51. Sakalli, I., Jusufi, K., Övgün, A.: Analytical solutions in a cosmic string Born–Infeld-dilaton black hole geometry: quasinormal modes and quantization. Gen. Relativ. Gravit. 50, 125 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  52. Chandrasekhar, S., Detweiler, S.: The quasi-normal modes of the Schwarzschild black hole. Proc. R. Soc. A 344, 441 (1975)

    Article  ADS  Google Scholar 

  53. Panotopoulos, G., Rincón, Á.: Greybody factors for a minimally coupled massless scalar field in Einstein–Born–Infeld dilaton spacetime. Phys. Rev. D 96, 025009 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  54. Page, D.N.: Dirac equation around a charged, rotating black hole. Phys. Rev. D 14, 1509 (1976)

    Article  ADS  Google Scholar 

  55. Newman, E., Penrose, R.: An approach to gravitational radiation by a method of spin coefficients. J. Math. Phys. (N. Y.) 3, 566–578 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  56. Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists. Elsevier Academic Press, Cambridge (2005)

    MATH  Google Scholar 

  57. Abramowitz, M.: Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables. Dover Publications Incorporated, Mineola (1974)

    MATH  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11875025.

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  1. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Yiqin Chen & Jiliang Jing

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Chen, Y., Jing, J. Quasinormal modes of Dirac field in Einstein–Born–Infeld dilaton black hole. Gen Relativ Gravit 51, 73 (2019). https://doi.org/10.1007/s10714-019-2554-x

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