Nonsingular black hole chemistry

Abstract

We study the nonsingular black hole in Anti de-Sitter background taking the negative cosmological constant as the pressure of the system. We investigate the horizon structure, and find the critical values $m_0$ and $\tilde{k}_0$, such that $m>m_0$ (or $\tilde{k}<\tilde{k}_0$) corresponds to a black solution with two horizons, namely the Cauchy horizon $x_-$ and the event horizon $x_+$. For $m=m_0$ (or $\tilde{k}=\tilde{k}_0$), there exist an extremal black hole with degenerate horizon $x_0=x_{\pm}$ and for $m<m_0$ (or $\tilde{k}>\tilde{k}_0$), no black hole solution exists. In turn, we calculate the thermodynamical properties and by observing the behaviour of Gibb's free energy and specific heat, we find that this black hole solution exhibits first order (small to large black hole) and second order phase transition. Further, we study the $P-V$ criticality of system and then calculate the critical exponents showing that they are the same as those of the Van der Waals fluid.