Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Large D membrane for higher derivative gravity and black hole second law

  • 11 Accesses

Abstract

We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in 1/D upto linear order in the Gauss-Bonnet (GB) parameter β. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in 1/D but non-perturbatively in β for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev.D 48 (1993) R3427 [gr-qcI9307038] [INSPIRE].

  2. [2]

    V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev.D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].

  3. [3]

    S. Bhattacharjee, S. Sarkar and A.C. Wall, Holographic entropy increases in quadratic curvature gravity, Phys. Rev.D 92 (2015) 064006 [arXiv:1504.04706] [INSPIRE].

  4. [4]

    A.C. Wall, A Second Law for Higher Curvature Gravity, Int. J. Mod. Phys.D 24 (2015) 1544014 [arXiv:1504.08040] [INSPIRE].

  5. [5]

    X. Dong, Holographic Entanglement Entropy for General Higher Derivative Gravity, JHEP01 (2014) 044 [arXiv:1310.5713] [INSPIRE].

  6. [6]

    J. Camps, Generalized entropy and higher derivative Gravity, JHEP 03 (2014) 070 [arXiv:1310.6659] [INSPIRE].

  7. [7]

    S. Bhattacharyya, F.M. Haehl, N. Kundu, R. Loganayagam and M. Rangamani, Towards a second law for Lovelock theories, JHEP03 (2017) 065 [arXiv:1612.04024] [INSPIRE].

  8. [8]

    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].

  9. [9]

    R. Suzuki and K. Tanabe, Stationary black holes: Large D analysis, JHEP09 (2015) 193 [arXiv:1505.01282] [INSPIRE].

  10. [10]

    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].

  11. [11]

    R. Emparan, K. Izumi, R. Luna, R. Suzuki and K. Tanabe, Hydro-elastic Complementarity in Black Branes at large D, JHEP06 (2016) 117 [arXiv:1602.05752] [INSPIRE].

  12. [12]

    T. Andrade, C. Pantelidou and B. Withers, Large D holography with metric deformations, JHEP09 (2018) 138 [arXiv:1806.00306] [INSPIRE].

  13. [13]

    S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, JHEP04 (2016) 076 [arXiv:1504.06613] [INSPIRE].

  14. [14]

    S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A Charged Membrane Paradigm at Large D, JHEP04 (2016) 128 [arXiv:1511.03432] [INSPIRE].

  15. [15]

    Y. Dandekar, A. De, S. Mazumdar, S. Minwalla and A. Saha, The large D black hole Membrane Paradigm at first subleading order, JHEP12 (2016) 113 [arXiv:1607.06475] [INSPIRE].

  16. [16]

    S. Bhattacharyya, P. Biswas, B. Chakrabarty, Y. Dandekar and A. Dinda, The large D black hole dynamics in AdS/dS backgrounds, JHEP10 (2018) 033 [arXiv:1704.06076] [INSPIRE].

  17. [17]

    S. Bhattacharyya, P. Biswas and Y. Dandekar, Black holes in presence of cosmological constant: second order in \( \frac{1}{D} \), JHEP10 (2018) 171 [arXiv:1805.00284] [INSPIRE].

  18. [18]

    S. Kundu and P. Nandi, Large D gravity and charged membrane dynamics with nonzero cosmological constant, JHEP12 (2018) 034 [arXiv:1806.08515] [INSPIRE].

  19. [19]

    S. Bhattacharyya et al., Currents and Radiation from the large D Black Hole Membrane, JHEP05 (2017) 098 [arXiv:1611.09310] [INSPIRE].

  20. [20]

    A. Saha, The large D Membrane Paradigm For Einstein-Gauss-Bonnet Gravity, JHEP01 (2019) 028 [arXiv:1806.05201] [INSPIRE].

  21. [21]

    A. Kar, T. Mandal and A. Saha, The large D membrane paradigm for general four-derivative theory of gravity with a cosmological constant, JHEP08 (2019) 078 [arXiv:1904.08273] [INSPIRE].

  22. [22]

    B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet Black Strings at Large D, JHEP10 (2017) 123 [arXiv:1707.09766] [INSPIRE].

  23. [23]

    R. Emparan, R. Suzuki and K. Tanabe, Decoupling and non-decoupling dynamics of large D black holes, JHEP07 (2014) 113 [arXiv:1406.1258] [INSPIRE].

  24. [24]

    E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press, Cambridge U.K. (2004).

  25. [25]

    M.M. Caldarelli, O.J.C. Dias, R. Emparan and D. Klemm, Black Holes as Lumps of Fluid, JHEP04 (2009) 024 [arXiv:0811.2381] [INSPIRE].

  26. [26]

    Y. Dandekar, S. Kundu, S. Mazumdar, S. Minwalla, A. Mishra and A. Saha, An Action for and Hydrodynamics from the improved Large D membrane, JHEP09 (2018) 137 [arXiv:1712.09400] [INSPIRE].

  27. [27]

    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP09 (2012) 046 [arXiv:1203.3544] [INSPIRE].

  28. [28]

    M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev.D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].

  29. [29]

    R.C. Myers and J.Z. Simon, Black Hole Thermodynamics in Lovelock Gravity, Phys. Rev.D 38 (1988) 2434 [INSPIRE].

  30. [30]

    B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet Black Rings at Large D, JHEP07 (2018) 067 [arXiv:1805.03345] [INSPIRE].

  31. [31]

    J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, JHEP05 (2014) 147 [arXiv:1105.3733] [INSPIRE].

  32. [32]

    S. Bhattacharyya, P. Biswas and M. Patra, A leading-order comparison between fluid-gravity and membrane-gravity dualities, JHEP05 (2019) 022 [arXiv:1807.05058] [INSPIRE].

Download references

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

Author information

Correspondence to Yogesh Dandekar.

Additional information

ArXiv ePrint: 1910.10964

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dandekar, Y., Saha, A. Large D membrane for higher derivative gravity and black hole second law. J. High Energ. Phys. 2020, 83 (2020). https://doi.org/10.1007/JHEP02(2020)083

Download citation

Keywords

  • Black Holes
  • Classical Theories of Gravity