黑洞第一定律与视界约束：微分秩判据
Black-Hole First Laws and Horizon Constraints: A Differential Rank Criterion
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中文总结 AI 辅助
本文提出微分秩判据，明确视界方程热力学重写中变分关系与已施加约束的选择，证明第一定律余向量可表示性条件，并验证Kerr–Newman、旋转BTZ及NMG黑洞与视界约束精确对齐。
中文摘要 AI 辅助
视界方程的热力学重写形式取决于哪些关系被变分以及哪些关系已被施加。我们提出了一个微分秩判据，使这些选择变得明确。该构造使用一个稳态度规族，连同独立标记的径向曲面、由度规参数确定的物理荷，以及视界热力学量的指定延拓。一个第一定律余向量可被所选约束逐点表示，当且仅当它位于这些约束微分的张成空间中。我们将这一代数条件与邻域中的光滑恒等式区分开来。若正则约束已定义完整的物理族，则逐点可表示性由第一定律本身推出；邻域恒等式则额外依赖于所选的延拓。在显式规定下，Kerr–Newman、新大质量引力中的旋转BTZ黑洞以及新型NMG黑洞均与其视界约束精确对齐。相比之下，将精确度规族代入场方程分量可在测试任何视界条件之前湮灭该残差。我们还给出了显式的熵–体积比较，并明确了固定系综数据在自由能变分中的作用。该框架将已确立的第一定律的推论与关于所选约束及其延拓的额外主张区分开来。
英文摘要
Thermodynamic rewritings of horizon equations depend on which relations are varied and which have already been imposed. We formulate a differential rank criterion that makes these choices explicit. The construction uses a stationary metric family together with an independently marked radial surface, physical charges determined by the metric parameters, and specified extensions of the horizon thermodynamic quantities. A first-law covector is pointwise representable by selected constraints precisely when it lies in the span of their differentials. We distinguish this algebraic condition from a smooth identity in a neighborhood. If regular constraints already define the complete physical family, pointwise representability follows from the first law itself; a neighborhood identity additionally depends on the chosen extensions. With explicit prescriptions, Kerr--Newman, rotating BTZ black holes in new massive gravity, and the new-type NMG black hole all exhibit exact alignment with their horizon constraints. By contrast, substituting an exact metric family into a field-equation component can annihilate that residual before any horizon condition is tested. We also give an explicit entropy--volume comparison and specify the role of fixed ensemble data in free-energy variations. The framework separates consequences of the established first law from additional claims about selected constraints and their extensions.
发表机构
- Department of Physics and Astronomy, Sejong University（世宗大学物理与天文系）
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