Abstract
In this paper, we study various aspects of the equilibrium thermodynamic state space geometry of AdS black holes. We first examine the Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context, the state space scalar curvature of these black holes is analysed in various regions of their thermodynamic parameter space. This provides important new insights into the structure and significance of the scalar curvature. We further investigate critical phenomena, and the behaviour of the scalar curvature near criticality, for KN-AdS black holes in two mixed ensembles, introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The critical exponents are identical to those in the RN-AdS and Kerr-AdS cases in the canonical ensemble. This suggests an universality in the scaling behaviour near critical points of AdS black holes. Our results further highlight qualitative differences in the thermodynamic state space geometry for electric charge and angular momentum fluctuations in these black holes.
Similar content being viewed by others
References
R.M. Wald, The thermodynamics of black holes, Living Rev. Rel. 4 (2001) 6 [gr-qc/9912119] [SPIRES].
D.N. Page, Hawking radiation and black hole thermodynamics, New J. Phys. 7 (2005) 203 [hep-th/0409024] [SPIRES].
R. Brout, S. Massar, R. Parentani and P. Spindel, A primer for black hole quantum physics, Phys. Rept. 260 (1995) 329 [arXiv:0710.4345] [SPIRES].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [SPIRES].
L. Tisza, Generalized thermodynamics, MIT P ress, Cambridge MA U.S.A. (1966).
H.B. Callen, Thermodynamics and an introcution to thermostatitics, Wiley, New York (1985).
F. Weinhold, Metric geometry of equilibrium thermodynamics, J. Chem Phys. 63 (1975) 2479.
F. Weinhold, Metric geometry of equilibrium thermodynamics. II. Scaling, homogeneity, and generalized Gibbs-Duhem relations, J. Chem Phys. 63 (1975) 2484.
G. Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys. 67 (1995) 605 [Erratum ibid. 68 (1996) 313] [SPIRES].
S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [SPIRES].
A. Sahay, T. Sarkar and G. Sengupta, Thermodynamic geometry and phase transitions in Kerr-Newman-AdS black holes, JHEP 04 (2010) 118 [arXiv:1002.2538] [SPIRES].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [SPIRES].
X.N. Wu, Multicritical phenomena of Reissner-Nordstrom anti-de Sitter black holes, Phys. Rev. D 62 (2000) 124023 [SPIRES].
H. Janyszek and R. Mrugala, Geometrical structure of the state space in classical statistical and phenomenological thermodynamics, Rep. Math. Phys. 27 (1989) 145.
B. Mirza and H. Mohammadzadeh, Ruppeiner geometry of anyon gas, Phys. Rev. E 78 (2008) 021127 [arXiv:0808.0241] [SPIRES].
G. Ruppeiner, Riemannian geometric approach to critical points: general theory, Phys. Rev. E 57 (1997) 5135.
M.M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav. 17 (2000) 399 [hep-th/9908022] [SPIRES].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [SPIRES].
R.A. Konoplya and A. Zhidenko, Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes, Phys. Rev. D 78 (2008) 104017 [arXiv:0809.2048] [SPIRES].
J.E. Aman, I. Bengtsson and N. Pidokrajt, Geometry of black hole thermodynamics, Gen. Rel. Grav. 35 (2003) 1733 [gr-qc/0304015] [SPIRES].
H. Janyszek, Riemannian geometry and stability of thermodynamical equilibrium systems, J. Phys. A: Math. Gen. 23 (1990) 477.
D. Brody and N. Rivier, Geometrical aspects of statistical mechanics, Phys. Rev. E 51 (1995) 1006 [SPIRES].
H.E. Stanley, Scaling, universality, and renormalization: three pillars of modern critical phenomena, Rev. Mod. Phys. 71 (1999) S358 [SPIRES].
M.E. Fisher, Scaling, Universality and Renormalization Group Theory, Lect. Notes Phys. 186 (1983).
C.O. Lousto, The Fourth law of black hole thermodynamics, Nucl. Phys. B 410 (1993) 155 [Erratum ibid. B 449 (1995) 433] [gr-qc/9306014] [SPIRES].
G. Ruppeiner, Stability and fluctuations in black hole thermodynamics, Phys. Rev. D 75 (2007) 024037 [SPIRES].
G. Ruppeiner, Thermodynamic curvature and phase transitions in Kerr-Newman black holes, Phys. Rev. D 78 (2008) 024016 [arXiv:0802.1326] [SPIRES].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [SPIRES].
G.W. Gibbons, M.J. Perry and C.N. Pope, The first law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sahay, A., Sarkar, T. & Sengupta, G. On the thermodynamic geometry and critical phenomena of AdS black holes. J. High Energ. Phys. 2010, 82 (2010). https://doi.org/10.1007/JHEP07(2010)082
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2010)082