Abstract
We obtain the quasinormal modes for tensor perturbations of Gauss–Bonnet (GB) black holes in d = 5, 7, 8 dimensions and vector perturbations in d = 5, 6, 7 and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in d = 6 is not considered because of the fact that the black hole is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss–Bonnet coupling (α′) increases. The imaginary part first decreases upto a certain value of α′ and then increases with α′ for both tensor and vector perturbations. For larger values of α′, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as α′ → 0, the quasinormal frequencies for tensor and vector perturbations of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.
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Kokkotas K.D. and Schmidt B.G. (1999). Living Rev. Rel. 2: 2
Nollert H.-P. (1999). Class. Quantum Grav. 16: R159
Regge T. and Wheeler J.A. (1957). Phys. Rev. 108: 1063
Zerilli F.J. (1970). Phys. Rev. D2: 2141
Vishveshwara C.V. (1970). Phys. Rev. D1: 2870
Vishveshwara C.V. (1970). Nature 227: 936
Kokkotas, K.D., Stergioulas, N.: In: Mouråo A.M., et al. (eds.). Proceedings of the 5th International, Workshop on New Worlds in Astroparticle Physics, Faro, Portugal, 8–10 January 2005. World Scientific, Singapore (2006)
Birmingham D., Sachs I. and Solodukhin S.N. (2002). Phys. Rev. Lett. 88: 151301
Birmingham D., Sachs I. and Solodukhin S.N. (2003). Phys. Rev. D67: 104026
Hod S. (1998). Phys. Rev. Lett. 81: 4293
Dreyer O. (2003). Phys. Rev. Lett. 90: 081301
Motl L. and Neitzke A. (2003). Adv. Theor. Math. Phys. 7: 307
Das S. and Shankaranarayanan S. (2005). Class. Quantum Grav. 22: L7
Ghosh A., Shankaranarayanan S. and Das S. (2006). Class. Quantum Grav. 23: 1851
Natário J. and Schiappa R. (2004). Adv. Theor. Math. Phys. 8: 1001
Sen A. (2006). JHEP 0603: 008
Moura F. and Schiappa R. (2007). Class. Quantum Grav. 24: 361
Scherk J. and Schwarz J.H. (1974). Nucl. Phys. B81: 118
Zwiebach B. (1985). Phys. Lett B156: 315
Boulware D.G. and Deser S. (1985). Phys. Rev. Lett. 55: 2656
Wheeler J.T. (1986). Nucl. Phys. B268: 737
Wheeler J.T. (1986). Nucl. Phys. B273: 732
Wiltshire D.L. (1988). Phys. Rev. D38: 2445
Meissner K.A. and Olechowski M. (2002). Phys. Rev. D65: 064017
Cvetic M., Nojiri S. and Odintsov S.D. (2002). Nucl. Phys. B628: 295
Nojiri S., Odintsov S.D. and Ogushi S. (2002). Phys. Rev. D65: 023521
Cho Y.M. and Neupane I.P. (2002). Phys. Rev. D66: 024044
Neupane I.P. (2003). Phys. Rev. D 67: 061501
Cai R.G. (2004). Phys. Lett. B582: 237
Clunan T., Ross S.F. and Smith D.J. (2004). Class. Quantum Grav. 21: 3447
Barrau A., Grain J. and Alexeyev S.O. (2004). Phys. Lett. B584: 114
Iyer B.R., Iyer S. and Vishveshwara C.V. (1989). Class. Quantum Grav. 6: 1627
Konoplya R. (2005). Phys. Rev. D71: 024038
Abdalla E., Konoplya R.A. and Molina C. (2005). Phys. Rev. D72: 084006
Iyer S. (1987). Phys. Rev. D35: 3632
Dotti G. and Gleiser R.J. (2005). Class. Quantum Grav. 22: L1
Gleiser R.J. and Dotti G. (2005). Phys. Rev. D72: 124002
Higuchi A. (1987). J. Math. Phys. 28: 1553
Rubin M.A. and Ordóñez C.R. (1984). J. Math. Phys. 25: 2888
Ishibashi A. and Kodama H. (2003). Prog. Theor. Phys. 110: 701
Kodama H. and Ishibashi A. (2003). Prog. Theor. Phys. 110: 901
Chandrasekhar S. and Detweiler S. (1975). Proc. Roy. Soc. (London) A344: 441
Ferrari V. and Mashhoon B. (1984). Phys. Rev. D30: 295
Schutz B. and Will C.M. (1988). J. Astrophys. 291: L33
Iyer S. and Will C.M. (1985). Phys. Rev. D35: 3621
Konoplya R.A. (2003). Phys.Rev. D68: 024018
Andersson N. (1992). Proc. R. Soc. (London) A439: 47
Andersson N. and Linnaeus S. (1992). Phys. Rev. D46: 4179
Leaver E.W. (1985). Proc. R. Soc. (London) A402: 285
Cardoso V., Lemos J.P.S. and Yoshida S. (2004). Phys. Rev. D69: 044004
Chakrabarti S.K. and Gupta K.S. (2006). Int. J. Mod. Phys. A21: 3565
Konoplya R.A. (2003). Phys. Rev. D68: 124017
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Chakrabarti, S.K. Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black hole using third order WKB approach. Gen Relativ Gravit 39, 567–582 (2007). https://doi.org/10.1007/s10714-007-0404-8
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DOI: https://doi.org/10.1007/s10714-007-0404-8