扩展相空间中(2+1)维AdS黑洞的物态方程

State Equation of (2+1) Dimensional AdS Black Hole in the Extended Phase Space

把宇宙学常数作为热力学压强,本文研究了扩展相空间中的(2+1)维AdS黑洞,得到了扩展相空间中物态方程的几何单位制形式和国际单位制形式.本文分别用解析方法和图像方法研究了该物态方程的行为.研究结果表明当且仅当Q=0时才与理想气体的状态方程相吻合,而当电荷Q取其他值时,与理想气体的曲线有一定偏差.研究结果还表明,(2+1)维AdS黑洞临界点条件方程组无法得到有物理意义的解,P-v图像也没有出现范德瓦尔斯气体的P-v图像特征.因此(2+1)维AdS黑洞在扩展相空间中的行为既不是严格的理想气体行为,也没有类范德瓦尔斯气体的行为.

Treating cosmological constant as thermodynamic pressure, state equation of （2 ＋ 1） dimen- sional AdS black hole in the extended phase space has been investigated in this paper. Both the geometric and physical expressions are derived. Analytic and graphical methods have been utilized to study the be- havior of the state equation. It is shown that the state equation coincides with that of ideal gas only when Q = 0 and it differs from the ideal gas curves for other values of Q. It is also shown that no physical solu- tion can be obtained from the condition of critical point and the curve does not show any behavior similar to the Van der Waals gas. So （2＋ 1） dimensional AdS black hole in the extended phase space behaves neither strictly as ideal gas nor as Van der Waals gas.