Abstract：The $P$–$v$ criticality and phase transition in the extended phase space of a noncommutative geometry-inspired Schwarzschild black hole in anti-de Sitter (AdS) spacetime are studied. The cosmological constant is treated as a dynamical pressure and its conjugate quantity is thermodynamic volume of the noncommutative geometry-inspired Schwarzschild-AdS black hole. The noncommutative parameter is also treated as a variable, and as a consequence, a new thermodynamic quantity $V_{\theta}$ conjugate to $P_{\theta}=-(8\pi \theta)^{-1}$ has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation. We find that the $P$–$v$ criticality and the small black hole/large black hole phase transition appear for the noncommutative Schwarzschild-AdS black hole. Numerical calculations indicate that the noncommutative parameter $\theta$ affects the phase transition as well as the critical temperature $T_{\rm c}$, horizon radius $r_{\rm +c}$ and pressure $P_{\rm c}$. However, the critical ratio $P_{\rm c}r_{\rm +c}/T_{\rm c}$ is universal (independent of $\theta$), which is very similar to the result in the van de Waals liquid–gas system, but different from that in the noncommutative geometry-inspired Reissner–Nordström-AdS black hole, where the critical ratio is no longer universal.
. [J]. 中国物理快报, 2017, 34(8): 80402-.
Jun Liang. The $P$–$v$ Criticality of a Noncommutative Geometry-Inspired Schwarzschild-AdS Black Hole. Chin. Phys. Lett., 2017, 34(8): 80402-.
2017, Vol. 34 
