Thermodynamic Instability of $\mathrm{{3D}}$ Einstein-Born-Infeld AdS Black Holes

TL;DR

This paper investigates the thermodynamic stability of 3D Einstein-Born-Infeld AdS black holes, finding that strong nonlinear electrodynamics effects can violate previous instability conjectures, indicating potential stability of super-entropic black holes.

Contribution

It provides a counterexample to the instability conjecture by analyzing the thermodynamics of nonlinear electrodynamics black holes in 3D AdS space.

Findings

Weak nonlinear effects support the instability conjecture.

Strong nonlinear effects can violate the conjecture.

Super-entropic black holes may be thermodynamically stable.

Abstract

Super-entropic black holes possess finite-area but noncompact event horizons and violate the reverse isoperimetric inequality. It has been conjectured that such black holes always have negative specific heat at constant volume $C_{V}$ or negative specific heat at constant pressure $C_{P}$ whenever $C_{V}>0$, making them unstable in extended thermodynamics. In this paper, we test this instability conjecture on a family of nonlinear electrodynamics black holes, namely $3$D Einstein-Born-Infeld (EBI) AdS black holes. Our results show that when nonlinear electrodynamics effects are weak, the instability conjecture is valid. However, the conjecture can be violated in some parameter region when nonlinear electrodynamics effects are strong enough. This observation thus provides a counter example to the instability conjecture, which suggests that super-entropic black holes could be thermodynamically stable.