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

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 → 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 Λ as the positive pressure, via P = −Λ/8π, of the system's thermodynamic properties of the nonsingular black hole with an AdS background. We find that for P < Pc, the black holes with CP > 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.