Static pure Lovelock black hole solutions with horizon topology S(n) × S(n)

  • Naresh Dadhich
  • Josep M. Pons
Open Access
Regular Article - Theoretical Physics


It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order N for topology S (n) × S (n). We thus obtain pure Lovelock static black hole solutions with two sphere topology for any order N, and in particular we study in full detail the third and fourth order Lovelock black holes. It is remarkable that thermodynamical stability of black hole discerns between odd and even N, and consequently between negative and positive Λ and it favors the former while rejecting the latter.


Classical Theories of Gravity Black Holes 


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.


  1. [1]
    N. Dadhich, S.G. Ghosh and S. Jhingan, The Lovelock gravity in the critical spacetime dimension, Phys. Lett. B 711 (2012) 196 [arXiv:1202.4575] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    N. Dadhich, Characterization of the Lovelock gravity by Bianchi derivative, Pramana 74 (2010) 875 [arXiv:0802.3034] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    D.G. Boulware and S. Deser, String generated gravity models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    J.T. Wheeler, Symmetric solutions to the maximally Gauss-Bonnet extended Einstein equations, Nucl. Phys. B 273 (1986) 732 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    J.T. Wheeler, Symmetric solutions to the Gauss-Bonnet extended Einstein equations, Nucl. Phys. B 268 (1986) 737 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    B. Whitt, Spherically symmetric solutions of general second order gravity, Phys. Rev. D 38 (1988) 3000 [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    M. Bañados, C. Teitelboim and J. Zanelli, Dimensionally continued black holes, Phys. Rev. D 49 (1994) 975 [gr-qc/9307033] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  8. [8]
    J. Crisostomo, R. Troncoso and J. Zanelli, Black hole scan, Phys. Rev. D 62 (2000) 084013 [hep-th/0003271] [INSPIRE].ADSMathSciNetGoogle Scholar
  9. [9]
    N. Dadhich, J.M. Pons and K. Prabhu, Thermodynamical universality of the Lovelock black holes, Gen. Rel. Grav. 44 (2012) 2595 [arXiv:1110.0673] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    X.O. Camanho and J.D. Edelstein, A Lovelock black hole bestiary, Class. Quant. Grav. 30 (2013) 035009 [arXiv:1103.3669] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    H. Maeda, S. Willison and S. Ray, Lovelock black holes with maximally symmetric horizons, Class. Quant. Grav. 28 (2011) 165005 [arXiv:1103.4184] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    H. Nariai, On some static solutions of Einsteins gravitational field equations in a spherically symmetric case, Sci. Rep. Tohoku Univ. 34 (1950) 160.ADSMathSciNetGoogle Scholar
  13. [13]
    H. Nariai, On a new cosmological solution of Einsteins field equations of gravitation, Sci. Rep. Tohoku Univ. 35 (1951) 62.MathSciNetMATHGoogle Scholar
  14. [14]
    G. Dotti and R.J. Gleiser, Obstructions on the horizon geometry from string theory corrections to Einstein gravity, Phys. Lett. B 627 (2005) 174 [hep-th/0508118] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    C. Bogdanos, C. Charmousis, B. Gouteraux and R. Zegers, Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem, JHEP 10 (2009) 037 [arXiv:0906.4953] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    G. Dotti, J. Oliva and R. Troncoso, Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory, Int. J. Mod. Phys. A 24 (2009) 1690 [arXiv:0809.4378] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    G. Dotti, J. Oliva and R. Troncoso, Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum, Phys. Rev. D 82 (2010) 024002 [arXiv:1004.5287] [INSPIRE].ADSMathSciNetGoogle Scholar
  18. [18]
    H. Maeda, Gauss-Bonnet black holes with non-constant curvature horizons, Phys. Rev. D 81 (2010) 124007 [arXiv:1004.0917] [INSPIRE].ADSGoogle Scholar
  19. [19]
    J.M. Pons and N. Dadhich, On static black holes solutions in Einstein and Einstein-Gauss-Bonnet gravity with topology SO(N) × SO(N), arXiv:1408.6754 [INSPIRE].
  20. [20]
    N. Dadhich, J.M. Pons and K. Prabhu, On the static Lovelock black holes, Gen. Rel. Grav. 45 (2013) 1131 [arXiv:1201.4994] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    B. Kol, Topology change in general relativity and the black hole black string transition, JHEP 10 (2005) 049 [hep-th/0206220] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    N. Farhangkhah and M. Dehghani, Lovelock black holes with nonmaximally symmetric horizons, Phys. Rev. D 90 (2014) 044014 [arXiv:1409.1410] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Centre for Theoretical PhysicsJamia Millia IslamiaNew DelhiIndia
  2. 2.Inter-University Centre for Astronomy and AstrophysicsPuneIndia
  3. 3.Departament d’Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos (ICCUB), Facultat de FísicaUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations