Phase transition and thermodynamical geometry of Reissner-Nordström-AdS black holes in extended phase space

Abstract

We study the thermodynamics and thermodynamic geometry of a five-dimensional Reissner-NordstromAdS black hole in the extended phase space by treating the cosmological constant as being related to the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. We find that the contribution of the charge of the black hole to the chemical potential is always positive, and the existence of charge makes the chemical potential become positive more easily. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric, and Quevedo metric, respectively, in the fixed N 2 case and the fixed q case. We find that in the fixed N 2 case, the divergence of the scalar curvature is related to the divergence of the specific heat with fixed electric potential in the Weinhold metric and Ruppeiner metric, and the divergence of the scalar curvature in the Quevedo metric corresponds to the divergence of the specific heat with fixed electric charge density. In the fixed q case, however, the divergence of the scalar curvature is related to the divergence of the specific heat with fixed chemical potential in the Weinhold metric and Ruppeiner metric, while in the Quevedo metric, the divergence of the scalar curvature corresponds to the divergence of the specific heat with a fixed number of colors and the vanishing of the specific heat with a fixed chemical potential.

Holographic black hole chemistry

“…As has already been emphasized in earlier work on holographic black hole chemistry [13][14][15][16][17], varying the cosmological constant Λ in the bulk essentially amounts to changing the number of colors in the field theory. Unlike changes in physical properties like the temperature and the chemical potential, the number of colors, N , is not a standard thermodynamical variable.…”

Thermodynamic geometry for charged Gauss-Bonnet black holes in AdS spacetimes

“…The Ruppeiner metric is equivalent to the metric introduced by Mrugula when restricted to Legendre submanifolds. There are some subtle issues which require Legendre invariance of thermodynamic metrics (see for example [65,66,67,68]) and connections between metrics derived from other potentials. We shall however not address such issues here.…”

On thermodynamics of charged AdS black holes in extended phases space via M2-branes background

“…According to the proposition reported in [1,[20][21][22], we consider the cosmological constant as the number of M2-branes in the M-theory background and its conjugate quantity as the associated chemical potential.…”

“…In this context, very recently the thermodynamics and thermodynamical geometry for five-dimensional AdS black holes in a type IIB superstring background known as Ad S 5 × S 5 [20][21][22] have been scrutinized. This geometry has been studied in many places in connection with the AdS/CFT correspondence providing a very useful framework to investigate such a geometry via the equivalence between gravitational theories in d-dimensional AdS space and conformal field theories (CFT) in a (d − 1)-dimensional boundary of such AdS spaces [23][24][25][26][27].…”