Skip to main content
SpringerLink
Log in

Cosmic censorship in Lovelock theory

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

In analyzing maximally symmetric Lovelock black holes with non-planar horizon topologies, many novel features have been observed. The existence of finite radius singularities, a mass gap in the black hole spectrum and solutions displaying multiple horizons are noteworthy examples. Naively, in all these cases, the appearance of naked singularities seems unavoidable, leading to the question of whether these theories are consistent gravity theories. We address this question and show that whenever the cosmic censorship conjecture is threaten, an instability generically shows up driving the system to a new configuration with presumably no naked singularities. Also, the same kind of instability shows up in the process of spherical black holes evaporation in these theories, suggesting a new phase for their decay. We find circumstantial evidence indicating that, contrary to many claims in the literature, the cosmic censorship hypothesis holds in Lovelock theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. C. Lanczos, A remarkable property of the Riemann-Christoffel tensor in four dimensions, Annals Math. 39 (1938) 842 [INSPIRE].

    Article  MathSciNet  Google Scholar 

  3. J.D. Edelstein, Lovelock theory, black holes and holography, in Progress in Mathematical Relativity, Gravitation and Cosmology, A. García-Parrado et al. eds., Springer Proc. Math. Stat. 60 (2013) 19 [arXiv:1303.6213] [INSPIRE].

  4. X.O. Camanho, J.D. Edelstein and J.M. Sánchez de Santos, Lovelock theory and the AdS/CFT correspondence, Gen. Rel. Grav. in press [arXiv:1309.6483] [INSPIRE].

  5. X.O. Camanho and J.D. Edelstein, A Lovelock black hole bestiary, Class. Quant. Grav. 30 (2013) 035009 [arXiv:1103.3669] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. C. Charmousis, Higher order gravity theories and their black hole solutions, Lect. Notes Phys. 769 (2009) 299 [arXiv:0805.0568] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. C. Garraffo and G. Giribet, The Lovelock black holes, Mod. Phys. Lett. A 23 (2008) 1801 [arXiv:0805.3575] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108 (1957) 1063 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. F.J. Zerilli, Effective potential for even parity Regge-Wheeler gravitational perturbation equations, Phys. Rev. Lett. 24 (1970) 737 [INSPIRE].

    Article  ADS  Google Scholar 

  10. S. Teukolsky, Rotating black holes — separable wave equations for gravitational and electromagnetic perturbations, Phys. Rev. Lett. 29 (1972) 1114 [INSPIRE].

    Article  ADS  Google Scholar 

  11. A. Ishibashi and H. Kodama, Perturbations and stability of static black holes in higher dimensions, Prog. Theor. Phys. Suppl. 189 (2011) 165 [arXiv:1103.6148] [INSPIRE].

    Article  ADS  Google Scholar 

  12. G. Dotti and R.J. Gleiser, Gravitational instability of Einstein-Gauss-Bonnet black holes under tensor mode perturbations, Class. Quant. Grav. 22 (2005) L1 [gr-qc/0409005] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. 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].

    MathSciNet  ADS  Google Scholar 

  14. 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].

    MathSciNet  ADS  Google Scholar 

  15. I.P. Neupane, Thermodynamic and gravitational instability on hyperbolic spaces, Phys. Rev. D 69 (2004) 084011 [hep-th/0302132] [INSPIRE].

    ADS  Google Scholar 

  16. M. Beroiz, G. Dotti and R.J. Gleiser, Gravitational instability of static spherically symmetric Einstein-Gauss-Bonnet black holes in five and six dimensions, Phys. Rev. D 76 (2007) 024012 [hep-th/0703074] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. R. 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].

    MathSciNet  ADS  Google Scholar 

  18. T. Takahashi and J. Soda, Stability of Lovelock black holes under tensor perturbations, Phys. Rev. D 79 (2009) 104025 [arXiv:0902.2921] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  19. T. Takahashi and J. Soda, Instability of small Lovelock black holes in even-dimensions, Phys. Rev. D 80 (2009) 104021 [arXiv:0907.0556] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  20. T. Takahashi and J. Soda, Master equations for gravitational perturbations of static Lovelock black holes in higher dimensions, Prog. Theor. Phys. 124 (2010) 911 [arXiv:1008.1385] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  21. T. Takahashi and J. Soda, Catastrophic instability of small Lovelock black holes, Prog. Theor. Phys. 124 (2010) 711 [arXiv:1008.1618] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  22. T. Takahashi and J. Soda, Pathologies in Lovelock AdS black branes and AdS/CFT, Class. Quant. Grav. 29 (2012) 035008 [arXiv:1108.5041] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. D.G. Boulware and S. Deser, String generated gravity models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].

    Article  ADS  Google Scholar 

  24. X.O. Camanho, J.D. Edelstein and M.F. Paulos, Lovelock theories, holography and the fate of the viscosity bound, JHEP 05 (2011) 127 [arXiv:1010.1682] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. R. Penrose, Gravitational collapse: the role of general relativity, Riv. Nuovo Cim. 1 (1969) 252 [Gen. Rel. Grav. 34 (2002) 1141] [INSPIRE].

  26. H. Maeda, Effects of Gauss-Bonnet terms on final fate of gravitational collapse, Class. Quant. Grav. 23 (2006) 2155 [gr-qc/0504028] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  27. H. Maeda, Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 73 (2006) 104004 [gr-qc/0602109] [INSPIRE].

    ADS  Google Scholar 

  28. M. Nozawa and H. Maeda, Effects of Lovelock terms on the final fate of gravitational collapse: analysis in dimensionally continued gravity, Class. Quant. Grav. 23 (2006) 1779 [gr-qc/0510070] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. M. Dehghani and N. Farhangkhah, Asymptotically flat radiating solutions in third order Lovelock gravity, Phys. Rev. D 78 (2008) 064015 [arXiv:0806.1426] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  30. P. Rudra, R. Biswas and U. Debnath, Gravitational collapse in generalized Vaidya space-time for Lovelock gravity theory, Astrophys. Space Sci. 335 (2011) 505 [arXiv:1101.0386] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  31. S. Ohashi, T. Shiromizu and S. Jhingan, Spherical collapse of inhomogeneous dust cloud in the Lovelock theory, Phys. Rev. D 84 (2011) 024021 [arXiv:1103.3826] [INSPIRE].

    ADS  Google Scholar 

  32. K. Zhou, Z.-Y. Yang, D.-C. Zou and R.-H. Yue, Spherically symmetric gravitational collapse of a dust cloud in third order Lovelock Gravity, Int. J. Mod. Phys. D 20 (2011) 2317 [arXiv:1107.2730] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. S. Ohashi, T. Shiromizu and S. Jhingan, Gravitational collapse of charged dust cloud in the Lovelock gravity, Phys. Rev. D 86 (2012) 044008 [arXiv:1205.5363] [INSPIRE].

    ADS  Google Scholar 

  34. R. Goswami and P.S. Joshi, Cosmic censorship in higher dimensions, Phys. Rev. D 69 (2004) 104002 [gr-qc/0405049] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  35. P.S. Joshi, Gravitational collapse and spacetime singularities, Cambridge University Press, Cambridge U.K. (2007).

    Book  MATH  Google Scholar 

  36. R. Zegers, Birkhoff ’s theorem in Lovelock gravity, J. Math. Phys. 46 (2005) 072502 [gr-qc/0505016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. H. Maeda, S. Willison and S. Ray, Lovelock black holes with maximally symmetric horizons, Class. Quant. Grav. 28 (2011) 165005 [arXiv:1103.4184] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. X.O. Camanho and J.D. Edelstein, Causality in AdS/CFT and Lovelock theory, JHEP 06 (2010) 099 [arXiv:0912.1944] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. J.T. Wheeler, Symmetric solutions to the Gauss-Bonnet extended Einstein equations, Nucl. Phys. B 268 (1986) 737 [INSPIRE].

    Article  ADS  Google Scholar 

  40. J.T. Wheeler, Symmetric solutions to the maximally Gauss-Bonnet extended Einstein equations, Nucl. Phys. B 273 (1986) 732 [INSPIRE].

    Article  ADS  Google Scholar 

  41. R. Aros, R. Troncoso and J. Zanelli, Black holes with topologically nontrivial AdS asymptotics, Phys. Rev. D 63 (2001) 084015 [hep-th/0011097] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  42. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. D. Wiltshire, Spherically symmetric solutions of Einstein-Maxwell theory with a Gauss-Bonnet term, Phys. Lett. B 169 (1986) 36 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. D.L. Wiltshire, Black holes in string generated gravity models, Phys. Rev. D 38 (1988) 2445 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  45. A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].

    Article  ADS  Google Scholar 

  46. R.C. Myers, A.O. Starinets and R.M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, JHEP 11 (2007) 091 [arXiv:0706.0162] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The viscosity bound and causality violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [INSPIRE].

    Article  ADS  Google Scholar 

  48. J. de Boer, M. Kulaxizi and A. Parnachev, AdS 7 /CFT 6 , Gauss-Bonnet gravity and viscosity bound, JHEP 03 (2010) 087 [arXiv:0910.5347] [INSPIRE].

    Article  Google Scholar 

  49. X.O. Camanho and J.D. Edelstein, Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity, JHEP 04 (2010) 007 [arXiv:0911.3160] [INSPIRE].

    Article  ADS  Google Scholar 

  50. J. de Boer, M. Kulaxizi and A. Parnachev, Holographic Lovelock gravities and black holes, JHEP 06 (2010) 008 [arXiv:0912.1877] [INSPIRE].

    Article  Google Scholar 

  51. J. Zanelli, Lecture notes on Chern-Simons (super-)gravities. Second edition (february 2008), hep-th/0502193 [INSPIRE].

  52. M. Bañados, C. Teitelboim and J. Zanelli, Dimensionally continued black holes, Phys. Rev. D 49 (1994) 975 [gr-qc/9307033] [INSPIRE].

    ADS  Google Scholar 

  53. J. Crisostomo, R. Troncoso and J. Zanelli, Black hole scan, Phys. Rev. D 62 (2000) 084013 [hep-th/0003271] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  54. P.R. Anderson, W.A. Hiscock and D.J. Loranz, Semiclassical stability of the extreme Reissner-Nordström black hole, Phys. Rev. Lett. 74 (1995) 4365 [gr-qc/9504019] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  55. D. Marolf, The dangers of extremes, Gen. Rel. Grav. 42 (2010) 2337 [arXiv:1005.2999] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. L. Vanzo, Black holes with unusual topology, Phys. Rev. D 56 (1997) 6475 [gr-qc/9705004] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  57. R.B. Mann, Black holes of negative mass, Class. Quant. Grav. 14 (1997) 2927 [gr-qc/9705007] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  58. O.J. Dias, G.T. Horowitz and J.E. Santos, Gravitational turbulent instability of anti-de Sitter space, Class. Quant. Grav. 29 (2012) 194002 [arXiv:1109.1825] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. X.O. Camanho, Lovelock gravity, black holes and holography, Ph.D. thesis, to appear, Santiago de Compostela Spain (2013).

  60. M.F. Paulos, Holographic phase space: c-functions and black holes as renormalization group flows, JHEP 05 (2011) 043 [arXiv:1101.5993] [INSPIRE].

    Article  ADS  Google Scholar 

  61. P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].

    Article  ADS  Google Scholar 

  62. M.W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett. 70 (1993) 9 [INSPIRE].

    Article  ADS  Google Scholar 

  63. S. Golod and T. Piran, Choptuik’s critical phenomenon in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 85 (2012) 104015 [arXiv:1201.6384] [INSPIRE].

    ADS  Google Scholar 

  64. N. Deppe, C. Leonard, T. Taves, G. Kunstatter and R. Mann, Critical collapse in Einstein-Gauss-Bonnet gravity in five and six dimensions, Phys. Rev. D 86 (2012) 104011 [arXiv:1208.5250] [INSPIRE].

    ADS  Google Scholar 

  65. X.O. Camanho, J.D. Edelstein, G. Giribet and A. Gomberoff, A new type of phase transition in gravitational theories, Phys. Rev. D 86 (2012) 124048 [arXiv:1204.6737] [INSPIRE].

    ADS  Google Scholar 

  66. X.O. Camanho, J.D. Edelstein, G. Giribet and A. Gomberoff, Generalized phase transition in Lovelock theory, to appear.

Download references

Author information

Authors and Affiliations

  1. Department of Particle Physics and IGFAE, University of Santiago de Compostela, E-15782, Santiago de Compostela, Spain

    Xián O. Camanho & José D. Edelstein

  2. Centro de Estudios Científicos, Valdivia, Chile

    José D. Edelstein

Authors
  1. Xián O. Camanho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José D. Edelstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José D. Edelstein.

Additional information

ArXiv ePrint: 1308.0304

Rights and permissions

Reprints and permissions

About this article

Cite this article

Camanho, X.O., Edelstein, J.D. Cosmic censorship in Lovelock theory. J. High Energ. Phys. 2013, 151 (2013). https://doi.org/10.1007/JHEP11(2013)151

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2013)151

Keywords

Search

Navigation