Thermodynamic instability of doubly spinning black objects

  • Dumitru AstefaneseiEmail author
  • Maria J. Rodriguez
  • Stefan Theisen


We investigate the thermodynamic stability of neutral black objects with (at least) two angular momenta. We use the quasilocal formalism to compute the grand canonical potential and show that the doubly spinning black ring is thermodynamically unstable. We consider the thermodynamic instabilities of ultra-spinning black objects and point out a subtle relation between the microcanonical and grand canonical ensembles. We also find the location of the black string/ membrane phases of doubly spinning black objects.


Black Holes Black Holes in String Theory 


  1. [1]
    M.J. Rodriguez, On the black hole species (by means of natural selection), arXiv:1003.2411 [SPIRES].
  2. [2]
    G.J. Galloway and R. Schoen, A generalization of Hawking’s black hole topology theorem to higher dimensions, Commun. Math. Phys. 266 (2006) 571 [gr-qc/0509107] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  3. [3]
    S. Hollands, A. Ishibashi and R.M. Wald, A higher dimensional stationary rotating black hole must be axisymmetric, Commun. Math. Phys. 271 (2007) 699 [gr-qc/0605106] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  4. [4]
    R. Emparan and H.S. Reall, A rotating black ring in five dimensions, Phys. Rev. Lett. 88 (2002) 101101 [hep-th/0110260] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  5. [5]
    A.A. Pomeransky and R.A. Sen’kov, Black ring with two angular momenta, hep-th/0612005 [SPIRES].
  6. [6]
    R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Ann. Phys. 172 (1986) 304 [SPIRES]. zbMATHCrossRefMathSciNetADSGoogle Scholar
  7. [7]
    D. Astefanesei, R.B. Mann, M.J. Rodriguez and C. Stelea, Quasilocal formalism and thermodynamics of asymptotically flat black objects, Class. Quant. Grav. 27 (2010) 165004 [arXiv:0909.3852] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  8. [8]
    G.T. Horowitz and A. Strominger, Black strings and P-branes, Nucl. Phys. B 360 (1991) 197 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  9. [9]
    R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  10. [10]
    O.J.C. Dias, P. Figueras, R. Monteiro, J.E. Santos and R. Emparan, Instability and new phases of higher-dimensional rotating black holes, Phys. Rev. D 80 (2009) 111701 [arXiv:0907.2248] [SPIRES].ADSGoogle Scholar
  11. [11]
    R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  12. [12]
    J.D. Brown and J.W. York, Jr., Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    S.R. Lau, Lightcone reference for total gravitational energy, Phys. Rev. D 60 (1999) 104034 [gr-qc/9903038] [SPIRES].ADSGoogle Scholar
  14. [14]
    R.B. Mann, Misner string entropy, Phys. Rev. D 60 (1999) 104047 [hep-th/9903229] [SPIRES].ADSGoogle Scholar
  15. [15]
    P. Kraus, F. Larsen and R. Siebelink, The gravitational action in asymptotically AdS and flat spacetimes, Nucl. Phys. B 563 (1999) 259 [hep-th/9906127] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  16. [16]
    B. Kleihaus, J. Kunz and E. Radu, New nonuniform black string solutions, JHEP 06 (2006) 016 [hep-th/0603119] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  17. [17]
    D. Astefanesei, M.J. Rodriguez and S. Theisen, Quasilocal equilibrium condition for black ring, JHEP 12 (2009) 040 [arXiv:0909.0008] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  18. [18]
    G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [SPIRES]. MathSciNetADSGoogle Scholar
  19. [19]
    D. Astefanesei and E. Radu, Quasilocal formalism and black ring thermodynamics, Phys. Rev. D 73 (2006) 044014 [hep-th/0509144] [SPIRES].MathSciNetADSGoogle Scholar
  20. [20]
    J.D. Brown, E.A. Martinez and J.W. York, Jr., Complex Kerr-Newman geometry and black hole thermodynamics, Phys. Rev. Lett. 66 (1991) 2281 [SPIRES]. zbMATHCrossRefMathSciNetADSGoogle Scholar
  21. [21]
    H. Elvang, R. Emparan and A. Virmani, Dynamics and stability of black rings, JHEP 12 (2006) 074 [hep-th/0608076] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  22. [22]
    R. Monteiro, M.J. Perry and J.E. Santos, Thermodynamic instability of rotating black holes, Phys. Rev. D 80 (2009) 024041 [arXiv:0903.3256] [SPIRES].MathSciNetADSGoogle Scholar
  23. [23]
    D.N. Page, Hawking radiation and black hole thermodynamics, New J. Phys. 7 (2005) 203 [hep-th/0409024] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  24. [24]
    O.J.C. Dias, P. Figueras, R. Monteiro, H.S. Reall and J.E. Santos, An instability of higher-dimensional rotating black holes, JHEP 05 (2010) 076 [arXiv:1001.4527] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  25. [25]
    G. Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys. 67 (1995) 605 [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  26. [26]
    S.S. Gubser and I. Mitra, The evolution of unstable black holes in anti-de Sitter space, JHEP 08 (2001) 018 [hep-th/0011127] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  27. [27]
    H.S. Reall, Classical and thermodynamic stability of black branes, Phys. Rev. D 64 (2001) 044005 [hep-th/0104071] [SPIRES].MathSciNetADSGoogle Scholar
  28. [28]
    R.B. Mann and D. Marolf, Holographic renormalization of asymptotically flat spacetimes, Class. Quant. Grav. 23 (2006) 2927 [hep-th/0511096] [SPIRES].zbMATHCrossRefMathSciNetADSGoogle Scholar
  29. [29]
    R.B. Mann, D. Marolf and A. Virmani, Covariant counterterms and conserved charges in asymptotically flat spacetimes, Class. Quant. Grav. 23 (2006) 6357 [gr-qc/0607041] [SPIRES]. zbMATHCrossRefMathSciNetADSGoogle Scholar
  30. [30]
    D. Astefanesei, R.B. Mann and C. Stelea, Note on counterterms in asymptotically flat spacetimes, Phys. Rev. D 75 (2007) 024007 [hep-th/0608037] [SPIRES].MathSciNetADSGoogle Scholar
  31. [31]
    H. Elvang and M.J. Rodriguez, Bicycling black rings, JHEP 04 (2008) 045 [arXiv:0712.2425] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  32. [32]
    M. Durkee, Geodesics and Symmetries of Doubly-Spinning Black Rings, Class. Quant. Grav. 26 (2009) 085016 [arXiv:0812.0235] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  33. [33]
    P.T. Chrusciel, J. Cortier and A. G.-P. Gomez-Lobo, On the global structure of the Pomeransky-Senkov black holes, arXiv:0911.0802 [SPIRES].
  34. [34]
    M. Ba˜nados, C. Teitelboim and J. Zanelli, Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem, Phys. Rev. Lett. 72 (1994) 957 [gr-qc/9309026] [SPIRES]. zbMATHCrossRefMathSciNetADSGoogle Scholar
  35. [35]
    D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [SPIRES].MathSciNetADSGoogle Scholar
  36. [36]
    J. Evslin and C. Krishnan, Metastable black saturns, JHEP 09 (2008) 003 [arXiv:0804.4575] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  37. [37]
    J.E. Aman and N. Pidokrajt, Geometry of higher-dimensional black hole thermodynamics, Phys. Rev. D 73 (2006) 024017 [hep-th/0510139] [SPIRES].MathSciNetADSGoogle Scholar
  38. [38]
    R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The phase structure of higher-dimensional black rings and black holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [SPIRES]. CrossRefMathSciNetADSGoogle Scholar
  39. [39]
    R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Blackfolds, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  40. [40]
    G. Arcioni and E. Lozano-Tellechea, Stability and critical phenomena of black holes and black rings, Phys. Rev. D 72 (2005) 104021 [hep-th/0412118] [SPIRES].MathSciNetADSGoogle Scholar
  41. [41]
    S. Lahiri and S. Minwalla, Plasmarings as dual black rings, JHEP 05 (2008) 001 [arXiv:0705.3404] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  42. [42]
    D. Astefanesei and H. Yavartanoo, Stationary black holes and attractor mechanism, Nucl. Phys. B 794 (2008) 13 [arXiv:0706.1847] [SPIRES].CrossRefMathSciNetADSGoogle Scholar
  43. [43]
    H.B. Callen, Thermodynamics and an introduction to thermostatistics, John Willey Sons (1985).Google Scholar

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Dumitru Astefanesei
    • 1
    Email author
  • Maria J. Rodriguez
    • 1
  • Stefan Theisen
    • 1
  1. 1.Max-Planck-Institut für GravitationsphysikAlbert-Einstein-InstitutGolmGermany

Personalised recommendations