Critical Phenomena and Reentrant Phase Transition of Asymptotically Reissner-Nordstrom Black Holes

TL;DR

This paper investigates how small nonlinear corrections to the Maxwell field affect the phase transitions of asymptotically Reissner-Nordström black holes, revealing reentrant phase transitions and new phase behaviors in extended phase space.

Contribution

It introduces a classification of black hole phase behavior based on a nonlinearity parameter, showing significant effects on phase structure and identifying conditions for reentrant phase transitions.

Findings

Reentrant phase transition occurs for q^{2}/7 > \u03b1

No phase transition below or at the critical point for q^{2}/7 = q^{2}/7

Small and large black holes are distinguishable at high temperatures and pressures

Abstract

By considering a small correction to the Maxwell field, we show that the resultant black hole solutions (also known as the asymptotically Reissner--Nordstr\"{o}m black holes) undergo the reentrant phase transition and can have a novel phase behavior. We also show that such a small nonlinear correction of the Reissner--Nordstr\"{o}m black holes has high effects on the phase structure of the solutions. It leads to a new classification in the canonical ensemble of extended phase space providing the values of the nonlinearity parameter $\alpha$ being $\alpha \lesseqqgtr 4q^{2}/7$. We shall study these three classes and investigate deviations from those of the standard Reissner--Nordstr\"{o}m solutions. Interestingly, we find that there is the reentrant phase transition for $\alpha <4q^{2}/7$, and for the case of $\alpha =4q^{2}/7$ there is no phase transition below (at) the critical point. For the last case, one finds that small and large black holes are thermodynamically distinguishable for temperatures and pressures higher than the critical ones.