Critical phenomena in the extended phase space of Kerr-Newman-AdS black holes

TL;DR

This paper explores the critical behavior of Kerr-Newman-AdS black holes in extended phase space, revealing how phase transition properties depend on charge and angular momentum, with potential implications for other thermodynamic systems.

Contribution

It provides a detailed numerical analysis and fitting formula for critical points, highlighting the dependence on the charge-angular momentum ratio and the continuous transition between different black hole phases.

Findings

Critical points depend on charge and angular momentum.

The coexistence curve varies with the ratio of angular momentum to charge squared.

Transition from Reissner-Nordström-AdS to Kerr-AdS black hole behavior as ratio changes.

Abstract

Treating the cosmological constant as a thermodynamic pressure, we investigate the critical behavior of a Kerr-Newman-AdS black hole system. The critical points for the van der Waals like phase transition are numerically solved. The highly accurate fitting formula for them is given and is found to be dependent of the charge $Q$ and angular momentum $J$. In the reduced parameter space, we find that the temperature, Gibbs free energy, and coexistence curve depend only on the dimensionless angular momentum-charge ratio $\epsilon=J/Q^2$ rather than $Q$ and $J$. Moreover, when varying $\epsilon$ from 0 to $\infty$, the coexistence curve will continuously change from that of the Reissner-Nordstr\"{o}m-AdS black hole to the Kerr-AdS black hole. These results may guide us to study the critical phenomena for other thermodynamic systems with two characteristic parameters.