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 \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.