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Scalar quasinormal modes for \(2+1\)-dimensional Coulomb-like AdS black holes from nonlinear electrodynamics

Abstract

We study the propagation of scalar fields in the background of \(2+1\)-dimensional Coulomb-like AdS black holes, and we show that such propagation is stable under Dirichlet boundary conditions. Then, we solve the Klein–Gordon equation by using the pseudospectral Chebyshev method and the Horowitz–Hubeny method, and we find the quasinormal frequencies. Mainly, we find that the quasinormal frequencies are purely imaginary for a null angular number and they are complex and purely imaginary for a non-null value of the angular number, which depend on the black hole charge, angular number and overtone number. On the other hand, the effect of the inclusion of a Coulomb-like field from nonlinear electrodynamics to general relativity for a vanishing angular number is the emergence of two branches of quasinormal frequencies in contrast with the static BTZ black hole.

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References

  1. 1.

    Banados, M., Teitelboim, C., Zanelli, J.: The Black hole in three-dimensional space-time. Phys. Rev. Lett. 69, 1849 (1992). arXiv:hep-th/9204099

  2. 2.

    Carlip, S.: The (2+1)-Dimensional black hole. Class. Quant. Gravit. 12, 2853 (1995). arXiv:gr-qc/9506079

  3. 3.

    Martinez, C., Teitelboim, C., Zanelli, J.: Charged rotating black hole in three space-time dimensions. Phys. Rev. D 61, 104013 (2000). arXiv:hep-th/9912259 [hepth]

  4. 4.

    Cataldo, M., Cruz, N., del Campo, S., Garcia, A.: (2+1)-dimensional black hole with Coulomb-like field. Phys. Lett. B 484, 154 (2000). arXiv:hep-th/0008138

  5. 5.

    Cataldo, M., González, P.A., Saavedra, J., Vásquez, Y., Wang, B.: Thermodynamics of (2+1)-dimensional Coulomb-like black holes from nonlinear electrodynamics with a traceless energy momentum tensor. Phys. Rev. D 103(2), 024047 (2021). arXiv:2010.06089 [gr-qc]

  6. 6.

    Hassaine, M., Martinez, C.: Higher-dimensional black holes with a conformally invariant Maxwell source. Phys. Rev. D 75, 027502 (2007). arXiv:hep-th/0701058 [hep-th]

  7. 7.

    Cardenas, M., Fuentealba, O., Martínez, C.: Three-dimensional black holes with conformally coupled scalar and gauge fields. Phys. Rev. D 90(12), 124072 (2014). arXiv:1408.1401 [hep-th]

  8. 8.

    Hassaine, M., Martinez, C.: Higher-dimensional charged black holes solutions with a nonlinear electrodynamics source. Class. Quant. Gravit. 25, 195023 (2008). arXiv:0803.2946 [hep-th]

  9. 9.

    Gurtug, O., Mazharimousavi, S.H., Halilsoy, M.: 2+1-dimensional electrically charged black holes in Einstein-power Maxwell Theory. Phys. Rev. D 85, 104004 (2012). arXiv:1010.2340 [gr-qc]

  10. 10.

    Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Dover Books on Mathematics, 2nd edn. Dover, Mineola (2001)

    MATH  Google Scholar 

  11. 11.

    Finazzo, S.I., Rougemont, R., Zaniboni, M., Critelli, R., Noronha, J.: Critical behavior of non-hydrodynamic quasinormal modes in a strongly coupled plasma. JHEP 1701, 137 (2017). arXiv:1610.01519 [hep-th]

  12. 12.

    Gonzalez, P.A., Vasquez, Y., Villalobos, R.N.: Perturbative and nonperturbative fermionic quasinormal modes of Einstein–Gauss–Bonnet-AdS black holes. Phys. Rev. D 98(6), 064030 (2018). arXiv:1807.11827 [gr-qc]

  13. 13.

    Bécar, R., González, P.A., Papantonopoulos, E., Vásquez, Y.: Quasinormal modes of three-dimensional rotating Ho\(\check{r}\)ava AdS black hole and the approach to thermal equilibrium. Eur. Phys. J. C 80(7), 600 (2020). arXiv:1906.06654 [gr-qc]

  14. 14.

    Aragón, A., González, P.A., Papantonopoulos, E., Vásquez, Y.: Anomalous decay rate of quasinormal modes in Schwarzschild-dS and Schwarzschild-AdS black holes. JHEP 2008, 120 (2020). [arXiv:2004.09386 [gr-qc]]

    ADS  MathSciNet  Article  Google Scholar 

  15. 15.

    Aragón, A., González, P.A., Papantonopoulos, E., Vásquez, Y.: Quasinormal modes and their anomalous behavior for black holes in \(f(R)\) gravity. arXiv:2005.11179 [gr-qc]

  16. 16.

    Aragón, A., Bécar, R., González, P.A., Vásquez, Y.: Massive Dirac quasinormal modes in Schwarzschild–de Sitter black holes: anomalous decay rate and fine structure. Phys. Rev. D 103(6), 064006 (2021). arXiv:2009.09436 [gr-qc]

  17. 17.

    Fontana, R.D.B., González, P.A., Papantonopoulos, E., Vásquez, Y.: Anomalous decay rate of quasinormal modes in Reissner–Nordström black holes. Phys. Rev. D 103(6), 064005 (2021). arXiv:2011.10620 [gr-qc]

  18. 18.

    Aragón, A., Bécar, R., González, P.A., Vásquez, Y.: Perturbative and nonperturbative quasinormal modes of 4D Einstein–Gauss–Bonnet black holes. Eur. Phys. J. C 80(8), 773 (2020). arXiv:2004.05632 [gr-qc]

  19. 19.

    Horowitz, G.T., Hubeny, V.E.: Quasinormal modes of AdS black holes and the approach to thermal equilibrium. Phys. Rev. D 62, 024027 (2000). arXiv:hep-th/9909056 [hep-th]

  20. 20.

    Dey, T.K.: Born-Infeld black holes in the presence of a cosmological arXiv:hep-th/0406169 [hep-th]

  21. 21.

    Cai, R.G., Pang, D.W., Wang, A.: Born–Infeld black holes in (A)dS spaces. Phys. Rev. D 70, 124034 (2004). arXiv:hep-th/0410158 [hep-th]

  22. 22.

    Boillat, G.: Nonlinear electrodynamics—Lagrangians and equations of motion. J. Math. Phys. 11(3), 941–951 (1970)

    ADS  Article  Google Scholar 

  23. 23.

    Fernando, S., Krug, D.: Charged black hole solutions in Einstein–Born–Infeld gravity with a cosmological constant. Gen. Relat. Gravit. 35, 129–137 (2003). arXiv:hep-th/0306120 [hep-th]

  24. 24.

    Jing, J., Chen, S.: Holographic superconductors in the Born–Infeld electrodynamics. Phys. Lett. B 686, 68–71 (2010). arXiv:1001.4227 [gr-qc]

  25. 25.

    de Oliveira, H.P.: Nonlinear charged black holes. Class. Quant. Gravit. 11, 1469–1482 (1994)

    ADS  MathSciNet  Article  Google Scholar 

  26. 26.

    Gullu, I., Sisman, T.C., Tekin, B.: Born–Infeld extension of new massive gravity. Class. Quant. Gravit. 27, 162001 (2010). arXiv:1003.3935 [hep-th]

  27. 27.

    Hendi, S.H., Eslam Panah, B., Saffari, R.: Exact solutions of three-dimensional black holes: Einstein gravity versus \(F(R)\) gravity. Int. J. Mod. Phys. D 23(11), 1450088 (2014). arXiv:1408.5570 [hep-th]

  28. 28.

    Hendi, S.H., Eslam Panah, B., Panahiyan, S.: Massive charged BTZ black holes in asymptotically (a)dS spacetimes. JHEP 05, 029 (2016). arXiv:1604.00370 [hep-th]

  29. 29.

    Hendi, S.H., Eslam Panah, B., Panahiyan, S., Sheykhi, A.: Dilatonic BTZ black holes with power-law field. Phys. Lett. B 767, 214–225 (2017). arXiv:1703.03403 [gr-qc]

  30. 30.

    Hossein Hendi, S., Eslam Panah, B., Panahiyan, S., Hassaine, M.: BTZ dilatonic black holes coupled to Maxwell and Born–Infeld electrodynamics. Phys. Rev. D 98(8), 084006 (2018). arXiv:1712.04328 [physics.gen-ph]

  31. 31.

    Hendi, S.H., Tavakkoli, A.M., Panahiyan, S., Eslam Panah, B., Hackmann, E.: Simulation of geodesic trajectory of charged BTZ black holes in massive gravity. Eur. Phys. J. C 80(6), 524 (2020). arXiv:2002.01302 [gr-qc]

  32. 32.

    Zou, D.C., Zhang, S.J., Wang, B.: Critical behavior of Born–Infeld AdS black holes in the extended phase space thermodynamics. Phys. Rev. D 89(4), 044002 (2014). arXiv:1311.7299 [hep-th]

  33. 33.

    Ayon-Beato, E., Garcia, A.: Regular black hole in general relativity coupled to nonlinear electrodynamics. Phys. Rev. Lett. 80, 5056–5059 (1998). arXiv:gr-qc/9911046 [gr-qc]

  34. 34.

    Regge, T., Wheeler, J.A.: Stability of a Schwarzschild singularity. Phys. Rev. 108, 1063 (1957)

    ADS  MathSciNet  Article  Google Scholar 

  35. 35.

    Konoplya, R.A., Zhidenko, A.: Quasinormal modes of black holes: from astrophysics to string theory. Rev. Mod. Phys. 83, 793 (2011). arXiv:1102.4014 [gr-qc]

  36. 36.

    Zerilli, F.J.: Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics. Phys. Rev. D 2, 2141 (1970)

    ADS  MathSciNet  Article  Google Scholar 

  37. 37.

    Zerilli, F.J.: Effective potential for even parity Regge–Wheeler gravitational perturbation equations. Phys. Rev. Lett. 24, 737 (1970)

    ADS  Article  Google Scholar 

  38. 38.

    Kokkotas, K.D., Schmidt, B.G.: Quasinormal modes of stars and black holes. Liv. Rev. Rel. 2, 2 (1999). arXiv:gr-qc/9909058

  39. 39.

    Nollert, H.-P.: Topical Review: quasinormal modes: the characteristic ‘sound’ of black holes and neutron stars. Class. Quant. Gravit. 16, R159 (1999)

  40. 40.

    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)

  41. 41.

    Maldacena, J.M.: The Large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231–252 (1998). arXiv:hep-th/9711200 [hep-th]

  42. 42.

    Aharony, O., Gubser, S.S., Maldacena, J.M., Ooguri, H., Oz, Y.: Large N field theories, string theory and gravity. Phys. Rep. 323, 183–386 (2000). arXiv:hep-th/9905111 [hep-th]

  43. 43.

    Konoplya, R.A.: On quasinormal modes of small Schwarzschild-anti-de Sitter black hole. Phys. Rev. D 66, 044009 (2002). arXiv:hep-th/0205142 [hep-th]

  44. 44.

    Cardoso, V., Konoplya, R., Lemos, J.P.S.: Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter space-times: a complete study on the asymptotic behavior. Phys. Rev. D 68, 044024 (2003). arXiv:gr-qc/0305037 [gr-qc]

  45. 45.

    Chan, J.S.F., Mann, R.B.: Scalar wave falloff in asymptotically anti-de Sitter backgrounds. Phys. Rev. D 55, 7546–7562 (1997)

    ADS  Article  Google Scholar 

  46. 46.

    Cardoso, V., Lemos, J.P.S.: Scalar, electromagnetic and Weyl perturbations of BTZ black holes: quasinormal modes. Phys. Rev. D 63, 124015 (2001). arXiv:gr-qc/0101052 [gr-qc]

  47. 47.

    Konoplya, R.A.: Influence of the back reaction of the Hawking radiation upon black hole quasinormal modes. Phys. Rev. D 70, 047503 (2004). arXiv:hep-th/0406100 [hep-th]

  48. 48.

    Gupta, K.S., Harikumar, E., Jurić, T., Meljanac, S., Samsarov, A.: Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole. JHEP 9, 25 (2015). arXiv:1505.04068 [hep-th]

  49. 49.

    Gupta, K.S., Jurić, T., Samsarov, A.: Noncommutative duality and fermionic quasinormal modes of the BTZ black hole. JHEP 06, 107 (2017). arXiv:1703.00514 [hep-th]

  50. 50.

    Becar, R., Gonzalez, P.A., Vasquez, Y.: Dirac quasinormal modes of two-dimensional charged dilatonic black holes. Eur. Phys. J. C 74, 2940 (2014). arXiv:1405.1509 [gr-qc]

  51. 51.

    Becar, R., Gonzalez, P.A., Vasquez, Y.: Quasinormal modes of four dimensional topological nonlinear charged Lifshitz black holes. Eur. Phys. J. C 76(2), 78 (2016). arXiv:1510.06012 [gr-qc]

  52. 52.

    González, P.A., Vásquez, Y.: Scalar Perturbations of nonlinear charged Lifshitz black branes with hyperscaling violation. Astrophys. Space Sci. 361(7), 224 (2016). arXiv:1509.00802 [hep-th]

  53. 53.

    González, P.A., Papantonopoulos, E., Saavedra, J., Vásquez, Y.: Superradiant instability of near extremal and extremal four-dimensional charged hairy black hole in anti-de Sitter spacetime. Phys. Rev. D 95(6), 064046. arXiv:1702.00439 [gr-qc]

  54. 54.

    Panotopoulos, G., Rincón, Á.: Quasinormal modes of black holes in Einstein-power-Maxwell theory. Int. J. Mod. Phys. D 27(3), 1850034 (2017). arXiv:1711.04146 [hep-th]

  55. 55.

    González, P.A., Övgün, A., Saavedra, J., Vásquez, Y.: Hawking radiation and propagation of massive charged scalar field on a three-dimensional Gödel black hole. Gen. Relat. Gravit. 50(6), 62 (2018). arXiv:1711.01865 [gr-qc]

  56. 56.

    Ćirić, M.D., Konjik, N., Samsarov, A.: Noncommutative scalar quasinormal modes of the Reissner–Nordström black hole. Class. Quant. Gravit. 35(17), 175005 (2018). arXiv:1708.04066 [hep-th]

  57. 57.

    Rincón, Á., Panotopoulos, G.: Quasinormal modes of scale dependent black holes in (1+2)-dimensional Einstein-power-Maxwell theory. Phys. Rev. D 97(2), 024027 (2018). arXiv:1801.03248 [hep-th]

  58. 58.

    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). arXiv:1801.08955 [gr-qc]

  59. 59.

    Panotopoulos, G., Rincón, Á.: Quasinormal modes of regular black holes with non linear-electrodynamical sources. Eur. Phys. J. Plus 134(6), 300 (2019). arXiv:1904.10847 [gr-qc]

  60. 60.

    Dimitrijević Ćirić, M., Konjik, N., Samsarov, A.: Noncommutative scalar field in the nonextremal Reissner–Nordström background: quasinormal mode spectrum. Phys. Rev. D 101(11), 116009 (2020). arXiv:1904.04053 [hep-th]

  61. 61.

    Myung, Y.S., Kim, Y.W., Park, Y.J.: Quasinormal modes from potentials surrounding the charged dilaton black hole. Eur. Phys. J. C 58, 617 (2008). arXiv:0809.1933 [gr-qc]

  62. 62.

    Cardoso, V., Lemos, J.P.S.: Quasinormal modes of Schwarzschild anti-de Sitter black holes: electromagnetic and gravitational perturbations. Phys. Rev. D 64, 084017 (2001). arXiv:gr-qc/0105103

  63. 63.

    Wolfram “Mathematica 10” (2015). http://www.wolfram.com

  64. 64.

    Birmingham, D., Sachs, I., Solodukhin, S.N.: Conformal field theory interpretation of black hole quasinormal modes. Phys. Rev. Lett. 88, 151301 (2002). arXiv:hep-th/0112055

  65. 65.

    Crisóstomo, J., Lepe, S., Saavedra, J.: Quasinormal modes of extremal BTZ black hole. Class. Quant. Gravit. 21, 2801–2810 (2004). arXiv:hep-th/0402048 [hep-th]

  66. 66.

    Becar, R., Gonzalez, P.A., Vasquez, Y.: Dirac quasinormal modes of Chern–Simons and BTZ black holes with torsion. Phys. Rev. D 89(2), 023001 (2014). arXiv:1306.5974 [gr-qc]

  67. 67.

    Wang, B., Lin, C.Y., Abdalla, E.: Quasinormal modes of Reissner–Nordstrom anti-de Sitter black holes. Phys. Lett. B 481, 79–88 (2000). arXiv:hep-th/0003295 [hep-th]

  68. 68.

    Berti, E., Kokkotas, K.D.: Quasinormal modes of Reissner–Nordström-anti-de Sitter black holes: scalar, electromagnetic and gravitational perturbations. Phys. Rev. D 67, 064020 (2003). arXiv:gr-qc/0301052 [gr-qc]

  69. 69.

    Richartz, M., Giugno, D.: Quasinormal modes of charged fields around a Reissner–Nordström black hole. Phys. Rev. D 90(12), 124011 (2014). arXiv:1409.7440 [gr-qc]

  70. 70.

    Richartz, M.: Quasinormal modes of extremal black holes. Phys. Rev. D 93(6), 064062 (2016). arXiv:1509.04260 [gr-qc]

  71. 71.

    Panotopoulos, G.: Charged scalar fields around Einstein-power-Maxwell black holes. Gen. Relat. Gravit. 51(6), 76 (2019)

    ADS  MathSciNet  Article  Google Scholar 

  72. 72.

    Cardoso, V., Costa, J.L., Destounis, K., Hintz, P., Jansen, A.: Quasinormal modes and strong cosmic censorship. Phys. Rev. Lett. 120(3), 031103 (2018). arXiv:1711.10502 [gr-qc]

  73. 73.

    Cardoso, V., Costa, J.L., Destounis, K., Hintz, P., Jansen, A.: Strong cosmic censorship in charged black-hole spacetimes: still subtle. Phys. Rev. D 98(10), 104007 (2018). arXiv:1808.03631 [gr-qc]

  74. 74.

    Destounis, K.: Charged fermions and strong cosmic censorship. Phys. Lett. B 795, 211–219 (2019). arXiv:1811.10629 [gr-qc]

  75. 75.

    Liu, H., Tang, Z., Destounis, K., Wang, B., Papantonopoulos, E., Zhang, H.: Strong cosmic censorship in higher-dimensional Reissner–Nordström–de Sitter spacetime. JHEP 03, 187 (2019). [arXiv:1902.01865 [gr-qc]]

    ADS  Article  Google Scholar 

  76. 76.

    Destounis, K.: Superradiant instability of charged scalar fields in higher-dimensional Reissner–Nordström–de Sitter black holes. Phys. Rev. D 100(4), 044054 (2019). arXiv:1908.06117 [gr-qc]

  77. 77.

    Destounis, K., Fontana, R.D.B., Mena, F.C., Papantonopoulos, E.: Strong cosmic censorship in Horndeski theory. JHEP 10, 280 (2019). arXiv:1908.09842 [gr-qc]

  78. 78.

    Destounis, K., Fontana, R.D.B., Mena, F.C.: Accelerating black holes: quasinormal modes and late-time tails. Phys. Rev. D 102(4), 044005 (2020). arXiv:2005.03028 [gr-qc]

  79. 79.

    Destounis, K., Fontana, R.D.B.: Stability of the Cauchy horizon in accelerating black-hole spacetimes. Phys. Rev. D 102(10), 104037 (2020). arXiv:2006.01152 [gr-qc]

  80. 80.

    Brito, R., Cardoso, V., Pani, P.: Superradiance: new frontiers in black hole physics. Lect. Notes Phys. 906, 1–237 (2015). arXiv:1501.06570 [gr-qc]

  81. 81.

    González, P.A., Rincón, Á, Saavedra, J., Vásquez, Y.: Superradiant instability and charged scalar quasinormal modes for \(2+1\)-dimensional Coulomb-like AdS black holes from nonlinear electrodynamics. arXiv:2107.08611 [gr-qc]

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Acknowledgements

We thank the referee for his/her careful review of the manuscript and his/her valuable comments and suggestions which helped us to improve the manuscript. This work is partially supported by ANID Chile through FONDECYT Grant No 1210635 (J. S.).

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Aragón, A., González, P.A., Saavedra, J. et al. Scalar quasinormal modes for \(2+1\)-dimensional Coulomb-like AdS black holes from nonlinear electrodynamics. Gen Relativ Gravit 53, 91 (2021). https://doi.org/10.1007/s10714-021-02864-6

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Keywords

  • Black holes
  • Quasinormal modes
  • Gravity in \(2+1\) dimensions