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Journal of High Energy Physics

, 2019:42 | Cite as

The fate of instability of de Sitter black holes at large D

  • Peng-Cheng Li
  • Cheng-Yong ZhangEmail author
  • Bin Chen
Open Access
Regular Article - Theoretical Physics
  • 245 Downloads

Abstract

We study non-linearly the gravitational instabilities of the Reissner- Nordstrom-de Sitter and the Gauss-Bonnet-de Sitter black holes by using the large D expansion method. In both cases, the thresholds of the instability are found to be con- sistent with the linear analysis, and on the thresholds the evolutions of the black holes under the perturbations settle down to stationary lumpy solutions. However, the solutions in the unstable region are highly time-dependent, and resemble the fully localized black spots and black ring with SD−2 and S1× SD−3 topologies, respectively. Our study indi- cates the possible transition between the lumpy black holes and the localized black holes in higher dimensions.

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. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett.70 (1993) 2837 [hep-th/9301052] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP09 (2003) 025 [hep-th/0308056] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    B. Kol, The phase transition between caged black holes and black strings: a review, Phys. Rept.422 (2006) 119 [hep-th/0411240] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    T. Harmark, V. Niarchos and N.A. Obers, Instabilities of black strings and branes, Class. Quant. Grav.24 (2007) R1 [hep-th/0701022] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    L. Lehner and F. Pretorius, Black Strings, low viscosity fluids and violation of cosmic censorship, Phys. Rev. Lett.105 (2010) 101102 [arXiv:1006.5960] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    R.A. Konoplya and A. Zhidenko, Instability of higher dimensional charged black holes in the de-Sitter world, Phys. Rev. Lett.103 (2009) 161101 [arXiv:0809.2822] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    R.A. Konoplya and A. Zhidenko, Instability of D-dimensional extremally charged Reissner-Nordstrom(-de Sitter) black holes: extrapolation to arbitrary D, Phys. Rev.D 89 (2014) 024011 [arXiv:1309.7667] [INSPIRE].ADSGoogle Scholar
  8. [8]
    M.A. Cuyubamba, R.A. Konoplya and A. Zhidenko, Quasinormal modes and a new instability of Einstein-Gauss-Bonnet black holes in the de Sitter world, Phys. Rev.D 93 (2016) 104053 [arXiv:1604.03604] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    C.-Y. Zhang, S.-J. Zhang, D.-C. Zou and B. Wang, Charged scalar gravitational collapse in de Sitter spacetime, Phys. Rev.D 93 (2016) 064036 [arXiv:1512.06472] [INSPIRE].ADSMathSciNetGoogle Scholar
  10. [10]
    R. Emparan, R. Suzuki and K. Tanabe, The large D limit of general relativity, JHEP06 (2013) 009 [arXiv:1302.6382] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    R. Emparan, R. Suzuki and K. Tanabe, Decoupling and non-decoupling dynamics of large D black holes, JHEP07 (2014) 113 [arXiv:1406.1258] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  12. [12]
    R. Emparan, T. Shiromizu, R. Suzuki, K. Tanabe and T. Tanaka, Effective theory of black holes in the 1/D expansion, JHEP06 (2015) 159 [arXiv:1504.06489] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  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].ADSMathSciNetzbMATHGoogle Scholar
  14. [14]
    R. Suzuki and K. Tanabe, Stationary black holes: large D analysis, JHEP09 (2015) 193 [arXiv:1505.01282] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    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
  16. [16]
    S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A charged membrane paradigm at large D, JHEP04 (2016) 128 [arXiv:1511.03432] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  17. [17]
    Y. Dandekar et al., The large D black hole membrane paradigm at first subleading order, JHEP12 (2016) 113 [arXiv:1607.06475] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    S. Bhattacharyya et al., The large D black hole dynamics in AdS/dS backgrounds, JHEP10 (2018) 033 [arXiv:1704.06076] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  19. [19]
    S. Bhattacharyya, P. Biswas and Y. Dandekar, Black holes in presence of cosmological constant: second order in 1 , JHEP10 (2018) 171 [arXiv:1805.00284] [INSPIRE].ADSzbMATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    S. Kundu and P. Nandi, Large D gravity and charged membrane dynamics with nonzero cosmological constant, JHEP12 (2018) 034 [arXiv:1806.08515] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  21. [21]
    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].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    B. Chen and P.-C. Li, Static gauss-bonnet black holes at large D, JHEP05 (2017) 025 [arXiv:1703.06381] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  23. [23]
    R. Suzuki and K. Tanabe, Non-uniform black strings and the critical dimension in the 1/D expansion, JHEP10 (2015) 107 [arXiv:1506.01890] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  24. [24]
    M. Rozali and A. Vincart-Emard, On brane instabilities in the large D limit, JHEP08 (2016) 166 [arXiv:1607.01747] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  25. [25]
    R. Emparan et al., Phases and stability of non-uniform black strings, JHEP05 (2018) 104 [arXiv:1802.08191] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  26. [26]
    V. Cardoso, I.P. Carucci, P. Pani and T.P. Sotiriou, Matter around Kerr black holes in scalar-tensor theories: scalarization and superradiant instability, Phys. Rev.D 88 (2013) 044056 [arXiv:1305.6936] [INSPIRE].ADSGoogle Scholar
  27. [27]
    C.-Y. Zhang, S.-J. Zhang and B. Wang, Superradiant instability of Kerr-de Sitter black holes in scalar-tensor theory, JHEP08 (2014) 011 [arXiv:1405.3811] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  28. [28]
    D. Marolf and A. Ori, Outgoing gravitational shock-wave at the inner horizon: the late-time limit of black hole interiors, Phys. Rev.D 86 (2012) 124026 [arXiv:1109.5139] [INSPIRE].ADSGoogle Scholar
  29. [29]
    C.P. Herzog, M. Spillane and A. Yarom, The holographic dual of a Riemann problem in a large number of dimensions, JHEP08 (2016) 120 [arXiv:1605.01404] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  30. [30]
    B. Chen, Z.-Y. Fan, P. Li and W. Ye, Quasinormal modes of Gauss-Bonnet black holes at large D, JHEP01 (2016) 085 [arXiv:1511.08706] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  31. [31]
    B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet black strings at large D, JHEP10 (2017) 123 [arXiv:1707.09766] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  32. [32]
    B. Chen, P.-C. Li, Y. Tian and C.-Y. Zhang, Holographic turbulence in Einstein-Gauss-Bonnet gravity at large D, JHEP01 (2019) 156 [arXiv:1804.05182] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  33. [33]
    B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet black rings at large D, JHEP07 (2018) 067 [arXiv:1805.03345] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  34. [34]
    A. Saha, The large D membrane paradigm for Einstein-Gauss-Bonnet gravity, JHEP01 (2019) 028 [arXiv:1806.05201] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  35. [35]
    X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, JHEP02 (2016) 020 [arXiv:1407.5597] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  36. [36]
    T. Andrade, R. Emparan and D. Licht, Rotating black holes and black bars at large D, JHEP09 (2018) 107 [arXiv:1807.01131] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  37. [37]
    T. Andrade, R. Emparan, D. Licht and R. Luna, Black hole collisions, instabilities and cosmic censorship violation at large D, JHEP09 (2019) 099 [arXiv:1908.03424] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  38. [38]
    P. Figueras, M. Kunesch, L. Lehner and S. Tunyasuvunakool, End point of the ultraspinning instability and violation of cosmic censorship, Phys. Rev. Lett.118 (2017) 151103 [arXiv:1702.01755] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    H. Bantilan, P. Figueras, M. Kunesch and R. Panosso Macedo, End point of nonaxisymmetric black hole instabilities in higher dimensions, Phys. Rev.D 100 (2019) 086014 [arXiv:1906.10696] [INSPIRE].ADSGoogle Scholar
  40. [40]
    O.J.C. Dias, J.E. Santos and B. Way, Lumpy AdS 5× S 5black holes and black belts, JHEP04 (2015) 060 [arXiv:1501.06574] [INSPIRE].ADSCrossRefMathSciNetzbMATHGoogle Scholar
  41. [41]
    O.J.C. Dias, J.E. Santos and B. Way, Localised AdS 5× S 5black holes, Phys. Rev. Lett.117 (2016) 151101 [arXiv:1605.04911] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    O.J.C. Dias et al., Instability and new phases of higher-dimensional rotating black holes, Phys. Rev.D 80 (2009) 111701 [arXiv:0907.2248] [INSPIRE].ADSGoogle Scholar
  43. [43]
    M. Shibata and H. Yoshino, Bar-mode instability of rapidly spinning black hole in higher dimensions: numerical simulation in general relativity, Phys. Rev.D 81 (2010) 104035 [arXiv:1004.4970] [INSPIRE].ADSGoogle Scholar
  44. [44]
    K. Tanabe, Charged rotating black holes at large D, arXiv:1605.08854 [INSPIRE].
  45. [45]
    T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
  46. [46]
    A.W. Peet and S.F. Ross, Microcanonical phases of string theory on AdS(m) x S**n, JHEP12 (1998) 020 [hep-th/9810200] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    V.E. Hubeny and M. Rangamani, Unstable horizons, JHEP05 (2002) 027 [hep-th/0202189] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    A. Buchel and L. Lehner, Small black holes in AdS 5× S 5 , Class. Quant. Grav.32 (2015) 145003 [arXiv:1502.01574] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  49. [49]
    C.P. Herzog and Y. Kim, The large dimension limit of a small black hole instability in Anti-de Sitter space, JHEP02 (2018) 167 [arXiv:1711.04865] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingP.R. China
  2. 2.School of Physics and AstronomySun Yat-sen UniversityZhuhaiP.R. China
  3. 3.Department of Physics and Siyuan LaboratoryJinan UniversityGuangzhouP.R. China
  4. 4.Center for High Energy PhysicsPeking UniversityBeijingP.R. China
  5. 5.Collaborative Innovation Center of Quantum MatterBeijingP.R. China

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