Abstract
The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure $P_{\mathrm{GB}}$. We studied the critical behavior associated with $P_{\mathrm{GB}}$ in the extended thermodynamic phase space at fixed cosmological constant and electric charge. The result shows that when the black holes are neutral, the associated critical points can only exist in five dimensional GB-AdS black holes with spherical topology, and the corresponding critical exponents are identical to those for Van der Waals system. For charged GB-AdS black holes, it is shown that there can be only one critical point in five dimensions (for black holes with either spherical or hyperbolic topologies), which also requires the electric charge to be bounded within some appropriate range; while in $d>5$ dimensions, there can be up to two different critical points at the same electric charge, and the phase transition can occur only at temperatures which are not in between the two critical values.
Highlights
Since the black hole enthalpy H is a homogeneous function of entropy S, electric charge Q, and thermodynamic pressures P and PGB, and as M scales as [length]d−3, S scales as [length]d−2, Q scales as [length]d−3, P and PGB scales as [length]−2, we find that the Smarr relation for the black hole under consideration reads (d − 3)H = (d −2)T S +(d − 3)Q − 2P V − 2PGBVGB. (13)
Taking the Gauss– Bonnet (GB) coupling α as a new thermodynamic variable PGB, we revisited the thermodynamics for GB-anti-de Sitter (AdS) black holes and studied the associated critical behavior at fixed electric charge and bare cosmological constant
It is shown that for static neutral GB-AdS black holes, the corresponding critical point exists only for black holes with spherical topology (i.e. k = +1) in five dimensions, and the set of critical exponents are identical to those of the Van der Waals system. This is quite similar to the P–V criticality associated with the cosmological constant at fixed GB coupling for the same black holes [22]
Summary
This picture has been substantially extended. The idea of including the variation of the cosmological constant in the first law of black hole thermodynamics has acquired increasing attention [14,15,16,17,18,19,20,21]. By studying the critical behaviors of AdS black holes in the extended phase space, i.e. the P–V diagram [22,23,24,25,26,27,28,29,30,31,32,33,34,35], where P is the thermodynamic pressure associated with the cosmological constant, which takes the value. We will consider the criticality associated with the new thermodynamic variables PGB and its conjugate VGB in the extended phase space of charged GB-AdS black holes. Some concluding remarks are given in the last section
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