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

Abstract

In this paper, we study the phase structure and equilibrium state space geometry of charged topological Gauss-Bonnet black holes in d-dimensional anti-de Sitter spacetime. Several critical points are obtained in the canonical ensemble, and the critical phenomena and critical exponents near them are examined. We find that the phase structures and critical phenomena drastically depend on the cosmological constant Λ and dimensionality d. The result also shows that there exists an analogy between the black hole and the van der Waals liquid gas system. Moreover, we explore the phase transition and possible property of the microstructure using the state space geometry. It is found that the Ruppeiner curvature diverges exactly at the points where the heat capacity at constant charge of the black hole diverges. This black hole is also found to be a multiple system, i.e., it is similar to the ideal gas of fermions in some range of the parameters, while to the ideal gas of bosons in another range.

Analytical and exact critical phenomena ofd-dimensional singly spinning Kerr-AdS black holes

“…Similar critical phenomena can also be found for the Kerr-Newman-AdS black hole [10]. Moreover, the critical phenomena were also found in the Q-Φ diagram for the charged AdS black hole [11,12], and for other AdS black holes [13][14][15].…”

Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space

“…Also, mass M is identified with enthalpy rather than with internal energy as long as P is included as a variable in the first law of thermodynamics. The critical behaviors of Reissner-Nordstrom-AdS and Gauss-Bonnet-AdS black holes in the canonical ensemble and an extended phase space are considered in [24,25,42].…”

“…The critical behaviors are analogous to the liquid-gas phase transition in the Van der Waals fluid. Also, it has been shown that the critical behavior of RNAdS and Gauss-Bonnet-AdS black holes at the vicinity of the critical point is similar to the Van der Waals fluid in both the nonextended phase space and the canonical ensemble [26,42]. Moreover, it is interesting to study the thermodynamic behavior of these charged AdS black holes in the extended phase space and an ensemble with pressure and electric potential Φ as the natural variables.…”

“…In these circumstances, the black hole mass known as an internal energy is replaced by enthalpy. Recently, the critical behavior of charged AdS black holes such as Reissner-Nordstrom-AdS and Kerr-Newman-AdS black holes has been investigated in the extended phase space (while the cosmological constant Λ is included as a thermodynamic variable) and in the canonical ensemble [24,25,42,43]. The critical behaviors are analogous to the liquid-gas phase transition in the Van der Waals fluid.…”

P−Vcriticality in the extended phase space of black holes in massive gravity

“…In this way, people can investigate the P -V critical behaviors of AdS black holes and find exactly the same behaviors as in the van der Waals liquid-gas system. The P -V criticality study of AdS black holes has now been pushed even further to other gravities such as higher-derivative gravities [19][20][21][22].…”