Nonsingular black hole chemistry in $4D$ Einstein-Gauss-Bonnet gravity

TL;DR

This paper constructs a nonsingular black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics in AdS space, analyzing its thermodynamics and phase transitions similar to Van der Waals fluids.

Contribution

It provides an exact static nonsingular black hole solution in 4D EGB gravity with nonlinear electrodynamics and explores its thermodynamic phase structure and critical behavior.

Findings

Black holes are thermodynamically stable for pressures below critical.

Phase transition from small unstable to large stable black holes occurs.

System exhibits Van der Waals-like critical exponents.

Abstract

The EGB is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in $ D > 4$ dimensions, and EGB gravity is topologically invariant in $4D$. Several ways have been proposed for regularizing the $ D \to 4 $ limit of EGB for non-trivial gravitational dynamics in $ 4D $. Motivated by the importance of AdS/CFT, we obtain an exact static spherically symmetric nonsingular black hole in $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED) in an AdS spacetime. We interpret the negative cosmological constant $\Lambda$ as the positive pressure, via $ P=-\Lambda/8\pi$, of the system's thermodynamic properties of the nonsingular black hole with an AdS background. We find that for $P<P_c$, the black holes with $C_P>0$ are stable to thermal fluctuations and unstable otherwise. We also analyzed the Gibbs free energy to find that the small globally unstable black holes undergo a phase transition to the large globally stable black holes. Further, we study the $P-V$ criticality of the system and then calculate the critical exponents to find that our system behaves like Van der Walls fluid.