Alternative approach to the critical behavior and microscopic structure of the power-Maxwell black holes

TL;DR

This paper introduces a new thermodynamic phase space approach to analyze higher-dimensional Power-Maxwell AdS black holes, revealing Van der Waals-like phase transitions, universal critical exponents, and strong repulsive microscopic interactions.

Contribution

It proposes fixing the cosmological constant while treating the black hole charge as a thermodynamic variable, offering new insights into black hole phase behavior and microscopic structure.

Findings

Black holes exhibit Van der Waals-like phase transitions.

Critical exponents match mean field theory predictions.

Microscopic interactions are strongly repulsive, increasing with dimensions.

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.