Critical behaviors and phase transitions of black holes in higher order gravities and extended phase spaces

TL;DR

This paper investigates the complex phase transition behaviors of higher-order gravity black holes in extended phase spaces, revealing reentrant, triple point, and Van der Waals-like transitions across various dimensions and ensembles.

Contribution

It introduces the analysis of critical behaviors and phase transitions of Gauss-Bonnet-Born Infeld-AdS black holes in extended phase space, including new types of phase transitions and their independence from certain parameters.

Findings

Reentrant and triple point phase transitions observed in specific ensembles.

Multiple reentrant phase transitions occur with increasing pressure.

Van der Waals behavior identified in higher dimensions.

Abstract

We consider the critical behaviors and phase transitions of Gauss Bonnet-Born Infeld-AdS black holes (GB-BI-AdS) for $d=5,6$ and the extended phase space. We assume the cosmological constant, $\Lambda$, the coupling coefficient $\alpha$, and the BI parameter $\beta$ to be thermodynamic pressures of the system. Having made these assumptions, the critical behaviors are then studied in the two canonical and grand canonical ensembles. We find "reentrant and triple point phase transitions" (RPT-TP) and "multiple reentrant phase transitions" (multiple RPT) with increasing pressure of the system for specific values of the coupling coefficient $\alpha$ in the canonical ensemble. Also, we observe a reentrant phase transition (RPT) of GB-BI-AdS black holes in the grand canonical ensemble and for $d=6$. These calculations are then expanded to the critical behavior of Born-Infeld-AdS (BI-AdS) black holes in the third order of Lovelock gravity and in the grand canonical ensemble to find a Van der Waals behavior for $d=7$ and a reentrant phase transition for $d=8$ for specific values of potential $\phi$ in the grand canonical ensemble. Furthermore, we obtain a similar behavior for the limit of $\beta \to \infty$, i.e charged-AdS black holes in the third order of the Lovelock gravity. Thus, it is shown that the critical behaviors of these black holes are independent of the parameter $\beta$ in the grand canonical ensemble.