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.

我们以反宇宙常数为系统压力，研究了反de-Sitter背景下的非奇异黑洞。我们调查地平线结构，并找到关键值${米}_0$ 和 ${\widetilde{ķ}}_0$，这样 $米>{米}_0$ （要么 $\widetilde{ķ}<{\widetilde{ķ}}_0$）对应于具有两个视界的黑色解，即柯西视界 $X_{-}$ 和事件范围 $X_{+}$。对于$米={米}_0$ （要么 $\widetilde{ķ}={\widetilde{ķ}}_0$），存在一个水平退化的极端黑洞 $X_0=X_{\pm }$ 和为 $米<{米}_0$ （要么 $\widetilde{ķ}>{\widetilde{ķ}}_0$），则不存在黑洞解决方案。反过来，我们计算了热力学性质，并通过观察吉布的自由能和比热的行为，发现该黑洞解决方案表现出一阶（小到大黑洞）和二阶相变。此外，我们研究了$P-V$ 系统的临界度，然后计算临界指数，表明它们与范德华斯流体的临界指数相同。