Quasinormal modes of Gauss-Bonnet black holes at large D

  • Bin ChenEmail author
  • Zhong-Ying Fan
  • Pengcheng Li
  • Weicheng Ye
Open Access
Regular Article - Theoretical Physics


Einstein’s General Relativity theory simplifies dramatically in the limit that the spacetime dimension D is very large. This could still be true in the gravity theory with higher derivative terms. In this paper, as the first step to study the gravity with a Gauss-Bonnet(GB) term, we compute the quasi-normal modes of the spherically symmetric GB black hole in the large D limit. When the GB parameter is small, we find that the non-decoupling modes are the same as the Schwarzschild case and the decoupled modes are slightly modified by the GB term. However, when the GB parameter is large, we find some novel features. We notice that there are another set of non-decoupling modes due to the appearance of a new plateau in the effective radial potential. Moreover, the effective radial potential for the decoupled vector-type and scalar-type modes becomes more complicated. Nevertheless we manage to compute the frequencies of the these decoupled modes analytically. When the GB parameter is neither very large nor very small, though analytic computation is not possible, the problem is much simplified in the large D expansion and could be numerically treated. We study numerically the vector-type quasinormal modes in this case.


Classical Theories of Gravity Black Holes 


Open Access

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  1. [1]
    R. Emparan, R. Suzuki and K. Tanabe, The large D limit of general relativity, JHEP 06 (2013) 009 [arXiv:1302.6382] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    R. Emparan, D. Grumiller and K. Tanabe, Large-D gravity and low-D strings, Phys. Rev. Lett. 110 (2013) 251102 [arXiv:1303.1995] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    R. Emparan and K. Tanabe, Holographic superconductivity in the large D expansion, JHEP 01 (2014) 145 [arXiv:1312.1108] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
  5. [5]
    E. Witten, Quarks, atoms, and the 1/N expansion, Phys. Today 33 (1980) 38.CrossRefGoogle Scholar
  6. [6]
    F.R. Tangherlini, Schwarzschild field in n dimensions and the dimensionality of space problem, Nuovo Cim. 27 (1963) 636 [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    R. Emparan and K. Tanabe, Universal quasinormal modes of large D black holes, Phys. Rev. D 89 (2014) 064028 [arXiv:1401.1957] [INSPIRE].ADSGoogle Scholar
  8. [8]
    R. Emparan, R. Suzuki and K. Tanabe, Instability of rotating black holes: large D analysis, JHEP 06 (2014) 106 [arXiv:1402.6215] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    R. Emparan, R. Suzuki and K. Tanabe, Decoupling and non-decoupling dynamics of large D black holes, JHEP 07 (2014) 113 [arXiv:1406.1258] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    R. Emparan, R. Suzuki and K. Tanabe, Quasinormal modes of (anti-)de Sitter black holes in the 1/D expansion, JHEP 04 (2015) 085 [arXiv:1502.02820] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, arXiv:1504.06613 [INSPIRE].
  12. [12]
    G. Giribet, Large D limit of dimensionally continued gravity, Phys. Rev. D 87 (2013) 107504 [arXiv:1303.1982] [INSPIRE].ADSGoogle Scholar
  13. [13]
    B. Zwiebach, Curvature squared terms and string theories, Phys. Lett. B 156 (1985) 315 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    D.G. Boulware and S. Deser, String generated gravity models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    G. Dotti and R.J. Gleiser, Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part I: tensor perturbations, Phys. Rev. D 72 (2005) 044018 [gr-qc/0503117] [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    R.J. Gleiser and G. Dotti, Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part II: vector and scalar perturbations, Phys. Rev. D 72 (2005) 124002 [gr-qc/0510069] [INSPIRE].ADSMathSciNetGoogle Scholar
  17. [17]
    R.G. Daghigh, G. Kunstatter and J. Ziprick, The mystery of the asymptotic quasinormal modes of Gauss-Bonnet black holes, Class. Quant. Grav. 24 (2007) 1981 [gr-qc/0611139] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    R.A. Konoplya and A. Zhidenko, (In)stability of D-dimensional black holes in Gauss-Bonnet theory, Phys. Rev. D 77 (2008) 104004 [arXiv:0802.0267] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A charged membrane paradigm at large D, arXiv:1511.03432 [INSPIRE].
  20. [20]
    B. Chen, Z.Y. Fan, P. Li and W. Ye, Quasinormal modes of charged Gauss-Bonnet black holes at large D, work in progress.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Bin Chen
    • 1
    • 2
    • 3
    Email author
  • Zhong-Ying Fan
    • 3
  • Pengcheng Li
    • 1
  • Weicheng Ye
    • 1
  1. 1.Department of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingP.R. China
  2. 2.Collaborative Innovation Center of Quantum MatterBeijingP.R. China
  3. 3.Center for High Energy PhysicsPeking UniversityBeijingP.R. China

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