标题： 与动态黑洞熵相关的表观视界 显示英文标题

标题： Apparent Horizons Associated with Dynamical Black Hole Entropy

摘要： 我们定义熵边缘外捕获表面（E-MOTSs）作为明显视界的一种推广。 然后我们证明，在围绕静态黑洞的一阶扰动下，Hollands、Wald 和 Zhang 提出的动态黑洞熵，在背景Killing视界上定义，可以表示为与之相关的E-MOTS上的Wall熵。 我们的结果确保了Hollands-Wald-Zhang熵在动态黑洞的每个静态阶段都退化为标准Wald熵，从而加强了动态熵公式的鲁棒性。 显示英文摘要

摘要： We define entropic marginally outer trapped surfaces (E-MOTSs) as a generalization of apparent horizons. We then show that, under first-order perturbations around a stationary black hole, the dynamical black hole entropy proposed by Hollands, Wald, and Zhang, defined on a background Killing horizon, can be expressed as the Wall entropy evaluated on an E-MOTS associated with it. Our result ensures that the Hollands-Wald-Zhang entropy reduces to the standard Wald entropy in each stationary regime of a dynamical black hole, thereby reinforcing the robustness of the dynamical entropy formulation.