暗能量背景下黑洞的全息相变

Holographic phase transition for a black hole in the background with dark energy

在暗能量背景下,研究了黑洞的热力学熵和纠缠熵的相结构.分别讨论了黑洞的电荷和暗能量态参数对黑洞相结构的影响.对于固定的暗能量态参数,当电荷的值增大时,黑洞热力学熵和纠缠熵的相结构与范德瓦尔斯相变的相结构完全类似,即黑洞先后经历一阶相变、二阶相变,最后达到稳定态.对于固定的电荷,当暗能量态参数增大时,黑洞热力学熵和纠缠熵的相结构并不完全类似.特别是,纠缠熵随暗能量态参数的变化与热力学熵的变化趋势完全相反.相同的是,当暗能量态参数增大时,在纠缠熵-温度平面和热力学熵-温度平面,黑洞都经历一阶相变和二阶相变.对于热力学熵和纠缠熵,发现在一阶相变的不稳定区域,麦克斯韦的等面积法则始终成立,在二阶相变临界点附近,热容的临界指数都是2/3.

In the background with dark energy, we investigate the phase structure of thermodynamic entropy and entanglement entropy. We investigate respectively the effect of the charge and state parameters of the dark energy on the phase structure of the black hole. For a fixed state parameter of dark energy, as the value of the charge increases, the phase structures of the thermodynamical entropy and the entanglement entropy are similar as that of the Van der Waals phase transition. That is, the black hole undergoes the first order phase transition and second order phase transition successively and reaches to a stable state at last. For a fixed charge, as the state parameter of dark energy increases, the phase structures of the thermodynamical entropy is not similar to the entanglement entropy. Especially, the tendency of the change of entanglement entropy with respect to the state parameter is opposite to the thermodynamic entropy. The same is that the black hole undergoes the first order phase transition and second order phase transition successively as the state parameter of dark energy increases. For the thermodynamics entropy and entanglement entropy, we find Maxwell＇s equal area law holds for the unstable region of the first order phase transition, and the critical exponent of the heat capacity is 2/3 near the critical points of the second order phase transition.