Critical Phenomena in Higher Curvature Charged AdS Black Holes

Abstract

In this paper we have studied the critical phenomena in higher curvature charged black holes in the anti-de Sitter (AdS) space-time. As an example we have considered the third order Lovelock-Born-Infeld black holes in seven dimensional AdS space-time. We have analytically derived the thermodynamic quantities of the system. Our analysis revealed the onset of a higher order phase transition in the black hole leading to an infinite discontinuity in the specific heat at constant charge at the critical points. Our entire analysis is based on the canonical framework where we have fixed the charge of the black hole. In an attempt to study the behaviour of the thermodynamic quantities near the critical points, we have derived the critical exponents of the system explicitly. Although, the values of the critical points have been determined numerically, the critical exponents are calculated analytically. Our results fit well with the thermodynamic scaling laws. The scaling hypothesis is also seen to be consistent with these scaling laws. We find that all types of AdS black holes, studied so far, indeed belong to the same universality class. Moreover, these results are consistent with the mean field theory approximation. We have also derived the suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface. * arindam.lala@bose.res.in arXiv:1205.6121v2 [gr-qc]

Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics

“…More interesting discoveries were obtained for the charged AdS black holes [6,7], where it was found that a first order small black hole and big black hole phase transition is allowed which is superficially analogous to a liquid-gas phase transition of the van der Waals fluid. This superficial reminiscence was also observed in other AdS backgrounds [8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes

“…Different from the RN-AdS black hole, there are two van der Waals-like critical points identified at different temperatures. The critical phenomena of Born-Infeld AdS black holes and higher curvature charged AdS black holes were investigated in [21][22][23], where the critical exponents were also examined. Treating the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, the critical behavior and P -V criticality of a charged AdS black hole is reexamined [24][25][26].…”

Gauss–Bonnet coupling constant as a free thermodynamical variable and the associated criticality

“…The asymptotically AdS charged black holes admit a gauge duality description via a dual thermal field theory. This dual description suggests that charged AdS black holes exhibit a critical behavior in the Q − φ diagram which is reminiscent of the liquid-gas phase transition a e-mail: xuweifuture@mail.nankai.edu.cn b e-mail: physicshx@gmail.com c e-mail: lzhao@nankai.edu.cn in a Van der Waals system [6][7][8][9][10][11][12][13], where Q and φ denote the electric charge and potential, respectively.…”