发表机构
School of Physics Science and Technology, Xinjiang University; Faculty of Science, Kunming University of Science and Technology（新疆大学物理科学与技术学院; 昆明理工大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过求解爱因斯坦引力与非线性电磁场耦合得到正则AdS黑洞，在施加正则条件后，发现其G-T图呈现8字形和C形结构，对应更丰富的一阶与零阶相变。
AI 中文摘要
我们通过求解爱因斯坦引力与宇宙学常数及非线性电磁场的耦合，得到了奇异的“母”黑洞解。首先在无约束相空间$(S, q, \alpha, P)$中推导“母”黑洞的热力学量，之后施加正则条件$M = q^3/\alpha$，自洽地得到一类球对称AdS正则黑洞的热力学量。我们区分两类热力学量：由第一定律定义的基本共轭变量，以及由它们构造的热力学响应函数。对于涉及二阶导数的响应函数——特别是热容——我们证明约束施加与导数计算的顺序不可互换，正确步骤是先施加约束再构造响应函数。在此框架下，我们发现当$P<P_c$时，$G$-$T$图展现出与标准RN-AdS黑洞的燕尾行为定性不同的行为。取而代之的是，对于$P<P_z$呈现8字形结构，对于$P_z<P<P_c$呈现C形结构，分别对应小黑洞与大黑洞相之间的一阶和零阶相变。因此，施加正则条件使得这类黑洞的相结构比标准RN-AdS情形更为丰富。
英文摘要
We obtain the singular ''mother'' black hole solution by solving the coupling between Einstein gravity with a cosmological constant and a nonlinear electromagnetic field. The thermodynamic quantities of the ''mother'' black hole are first derived in the unconstrained phase space $(S, q, α, P)$, after which the regularity condition $M = q^3/α$ is imposed to obtain the thermodynamic quantities of a class of spherically symmetric AdS regular black holes self-consistently. We distinguish two categories of thermodynamic quantities: fundamental conjugate variables defined by the first law, and thermodynamic response functions constructed from them. For response functions involving second-order derivatives -- in particular the heat capacity -- we show that the order of constraint imposition and derivative calculation cannot be interchanged, and the correct procedure is to first impose the constraint and then construct the response function. Within this framework, we find that when $P<P_c$, the $G$--$T$ diagram exhibits a behavior qualitatively different from the swallowtail behavior of the standard RN-AdS black hole. Instead, it exhibits an 8-shaped structure for $P<P_z$ and a C-shaped structure for $P_z<P<P_c$, corresponding to first-order and zeroth-order phase transitions between small and large black hole phases, respectively. Imposing the regularity condition thus leads to a richer phase structure for this class of black holes than the standard RN-AdS case.
Comments9 pages, 6 figures
