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Physics, General Physics, physics.gen-ph
Abstract:
Employing a new approach toward thermodynamic phase space, we investigate the
phase transition, critical behavior and microscopic structure of higher
dimensional black holes in an Anti-de Sitter (AdS) background and in the
presence of Power-Maxwell field. In contrast to the usual extended $P-V$ phase
space where the cosmological constant (pressure) is treated as a thermodynamic
variable, we fix the cosmological constant and treat the charge of the black
hole (or more precisely $Q^s$) as a thermodynamic variable. Based on this new
standpoint, we develop the resemblance between higher dimensional nonlinear
black hole and Van der Waals liquid-gas system. We write down the equation of
state as $% Q^s=Q^s(T,\psi)$, where $\psi$ is the conjugate of $Q^s$, and
construct a Smarr relation based on this new phase space as $M=M(S,P,Q^s)$,
while $% s=2p/(2p-1)$ and $p$ is the power parameter of the Power-Maxwell
Lagrangian. We obtain the Gibbs free energy of the system and find a
swallowtail behaviour in Gibbs diagrams, which is a characteristic of
first-order phase transition and express the analogy between our system and van
der Waals fluid-gas system. Moreover, we calculate the critical exponents and
show that they are independent of the model parameters and are the same as
those of Van der Waals system which is predicted by the mean field theory.
Finally , we successfully explain the microscopic behavior of the black hole by
using thermodynamic geometry. We observe a gap in the scalar curvature $R$
occurs between small and large black hole. The maximum amount of the gap
increases as the number of dimensions increases. We finally find that character
of the interaction among the internal constituents of the black hole
thermodynamic system is intrinsically a strong repulsive interaction.
