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The large D membrane paradigm for Einstein-Gauss-Bonnet gravity

  • Arunabha SahaEmail author
Open Access
Regular Article - Theoretical Physics
  • 28 Downloads

Abstract

We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in terms of membrane variables. We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations. We work out the light quasi-normal mode spectrum of static black holes in EGB gravity from the linearised fluctuations of static, round membranes. Also, the effective equations for stationary black holes and the spectrum of linearised spectrum about black string configurations has been obtained using the membrane equation for EGB gravity. All our results are worked out to linear order in the Gauss-Bonnet parameter.

Keywords

Black Holes Classical Theories of Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    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].ADSCrossRefzbMATHGoogle Scholar
  2. [2]
    S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, JHEP 04 (2016) 076 [arXiv:1504.06613] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  3. [3]
    S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A charged membrane paradigm at large D, JHEP 04 (2016) 128 [arXiv:1511.03432] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  4. [4]
    S. Bhattacharyya, P. Biswas, B. Chakrabarty, Y. Dandekar and A. Dinda, The large D black hole dynamics in AdS/dS backgrounds, JHEP 10 (2018) 033 [arXiv:1704.06076] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    S. Bhattacharyya, P. Biswas and Y. Dandekar, Black holes in presence of cosmological constant: second order in 1/D, JHEP 10 (2018) 171 [arXiv:1805.00284] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    Y. Dandekar, A. De, S. Mazumdar, S. Minwalla and A. Saha, The large D black hole membrane paradigm at first subleading order, JHEP 12 (2016) 113 [arXiv:1607.06475] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    R. Emparan, T. Shiromizu, R. Suzuki, K. Tanabe and T. Tanaka, Effective theory of black holes in the 1/D expansion, JHEP 06 (2015) 159 [arXiv:1504.06489] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    R. Suzuki and K. Tanabe, Stationary black holes: large D analysis, JHEP 09 (2015) 193 [arXiv:1505.01282] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    R. Suzuki and K. Tanabe, Non-uniform black strings and the critical dimension in the 1/D expansion, JHEP 10 (2015) 107 [arXiv:1506.01890] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    R. Emparan, R. Suzuki and K. Tanabe, Evolution and end point of the black string instability: large D solution, Phys. Rev. Lett. 115 (2015) 091102 [arXiv:1506.06772] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    K. Tanabe, Instability of the de Sitter Reissner-Nordstrom black hole in the 1/D expansion, Class. Quant. Grav. 33 (2016) 125016 [arXiv:1511.06059] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Y. Dandekar, S. Mazumdar, S. Minwalla and A. Saha, Unstableblack branesfrom scaled membranes at large D, JHEP 12 (2016) 140 [arXiv:1609.02912] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Y. Dandekar, S. Kundu, S. Mazumdar, S. Minwalla, A. Mishra and A. Saha, An action for and hydrodynamics from the improved large D membrane, JHEP 09 (2018) 137 [arXiv:1712.09400] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    R. Emparan, K. Izumi, R. Luna, R. Suzuki and K. Tanabe, Hydro-elastic complementarity in black branes at large D, JHEP 06 (2016) 117 [arXiv:1602.05752] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    C.P. Herzog, M. Spillane and A. Yarom, The holographic dual of a Riemann problem in a large number of dimensions, JHEP 08 (2016) 120 [arXiv:1605.01404] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    M. Rozali, E. Sabag and A. Yarom, Holographic turbulence in a large number of dimensions, JHEP 04 (2018) 065 [arXiv:1707.08973] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    M. Rozali and A. Vincart-Emard, On brane instabilities in the large D limit, JHEP 08 (2016) 166 [arXiv:1607.01747] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    C.P. Herzog and Y. Kim, The large dimension limit of a small black hole instability in anti-de Sitter space, JHEP 02 (2018) 167 [arXiv:1711.04865] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    B. Chen, Z.-Y. Fan, P. Li and W. Ye, Quasinormal modes of Gauss-Bonnet black holes at large D, JHEP 01 (2016) 085 [arXiv:1511.08706] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    B. Chen, P.-C. Li and Z.-Z. Wang, Charged black rings at large D, JHEP 04 (2017) 167 [arXiv:1702.00886] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  21. [21]
    B. Chen and P.-C. Li, Static Gauss-Bonnet black holes at large D, JHEP 05 (2017) 025 [arXiv:1703.06381] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  22. [22]
    B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet black strings at large D, JHEP 10 (2017) 123 [arXiv:1707.09766] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    B. Chen, P.-C. Li, Y. Tian and C.-Y. Zhang, Holographic turbulence in Einstein-Gauss-Bonnet gravity at large D, arXiv:1804.05182 [INSPIRE].
  24. [24]
    M. Mandlik and S. Thakur, Stationary solutions from the large D membrane paradigm, JHEP 11 (2018) 026 [arXiv:1806.04637] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    Y. Choquet-Bruhat, The Cauchy problem for stringy gravity, J. Math. Phys. 29 (1988) 1891 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    S. Bhattacharyya et al., Currents and radiation from the large D black hole membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.University of GenevaGeneve 4Switzerland
  2. 2.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia

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