发表机构
New Uzbekistan University; Ulugh Beg Astronomical Institute; Institute of Theoretical Physics, National University of Uzbekistan; School of Physics, Harbin Institute of Technology（新乌兹别克斯坦大学; 乌鲁伯格天文研究所; 乌兹别克斯坦国立大学理论物理研究所; 哈尔滨工业大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对正则黑洞热力学失配问题，证明标准第一定律在完整解空间成立，因子$\Xi$源于沿正则子族的投影，其倒数等于视界内质量比例，且修正项非闭形式。
AI 中文摘要
据报道，在广义相对论与非线性电动力学耦合下的正则黑洞，其热力学表现出明显的失配：沿正则度规族对质量求导所得的温度与霍金温度相差一个因子 $\Xi$，且第一定律似乎需要修正的熵或修正的内能。我们针对 $D\geq4$ 维中带电的正则黑洞族研究此问题，其度规在四维时退化为巴丁和哈亚德几何。源项写为具有固定耦合且不含解参数的哈密顿密度 $H(P)$。该理论具有两参数静态解族，其中正则度规构成单参数子族。我们解析地证明，在整个解空间上，标准热力学第一定律以霍金温度、面积熵和视界势成立，与非线性电动力学的一般第一定律一致。当沿固定长度参数的正则度规族对质量求导时，出现因子 $\Xi$，该变分在理论空间中移动并改变守恒荷。我们证明 $\Xi^{-1}$ 是该投影的雅可比行列式，等于视界内质量的比例，给出其对任意正则质量函数的一般形式，并证明 $\Xi^{-1}dM_{ADM}$ 在两参数度规族上不是闭的一次形式，因此该修正不能是局部状态函数的微分。我们还指出，在 $D\geq5$ 中，$F$ 与 $P$ 框架之间的勒让德映射在近极端解视界外的半径处退化。
英文摘要
Regular black holes in general relativity coupled to nonlinear electrodynamics have been reported to exhibit an apparent mismatch in their thermodynamics: the temperature obtained by differentiating the mass along the family of regular metrics differs from the Hawking temperature by a factor $Ξ$, and the first law seems to need a modified entropy or a corrected internal energy. We examine this question for an electrically charged family of regular black holes in $D\geq4$ dimensions whose metrics reduce to the Bardeen and Hayward geometries in four dimensions. The source is written as a Hamiltonian density $H(P)$ with fixed couplings and no solution parameters. This theory has a two-parameter family of static solutions, of which the regular metrics form a one-parameter subfamily. We prove analytically that on the whole solution space the standard first law of thermodynamics holds with the Hawking temperature, the area entropy and the horizon potential, in agreement with the general first law for nonlinear electrodynamics. The factor $Ξ$ appears when the mass is differentiated along the regular metric family at fixed length parameter, a variation that moves through the space of theories and also changes the conserved charge. We show that $Ξ^{-1}$ is the Jacobian of this projection, equal to the fraction of the mass inside the horizon, give its general form for an arbitrary regular mass function, and show that $Ξ^{-1}dM_{ADM}$ is not a closed one-form on the two-parameter metric family, so this correction cannot be the differential of a local state function there. We also point out that the Legendre map between the $F$ and $P$ frames degenerates at a radius that lies outside the horizon of near-extremal solutions in $D\geq5$.
Comments6 pages
