蒸发的史瓦西-反德西特黑洞中的动态类时纠缠熵
Dynamical Timelike Entanglement Entropy in an Evaporating Schwarzschild--AdS Black Hole
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中文总结 AI 辅助
研究蒸发的史瓦西-反德西特黑洞中的时间量子关联，通过扩展类时纠缠熵构建，利用霍金辐射与外部吸收浴建模，推导出累积热相位，构建动态类时纠缠熵，得到非均匀时间间隔等结果，建立了研究该问题的第一性原理动态框架。
中文摘要 AI 辅助
类时纠缠熵（tEE）最近成为引力系统中时间量子关联的一种新型探针。现有研究大多局限于静态背景。本文将tEE的构建扩展到蒸发的史瓦西-反德西特黑洞。通过霍金辐射与外部吸收浴的有效斯特藩-玻尔兹曼描述对蒸发进行建模，得到随时间变化的视界半径（$r_h(t)$）和表面引力$\kappa(t)$。从演化视界的近视界林德勒结构推导出静态克鲁斯卡尔构造的绝热推广，得到累积热相位$\Phi(t)=\int_0^t\kappa(t')\,dt'$作为静态相位$\kappa t$的自然替代。该构造的有效性由明确的绝热参数$\mathcal A(t)$控制，数值验证在整个感兴趣的区域内它都很小（$\lesssim0.012$）。在视界穿过从静态热力学独立确定的临界半径$r_h = l/\sqrt3$时它恰好消失。利用$\Phi(t)$，构建了动态类时纠缠熵，它连续跟踪蒸发过程并推导出相应的动态佩奇类时间。与静态几何中均匀间隔的佩奇类时间不同，蒸发导致时间间隔不均匀，同时类时纠缠熵的振荡存在渐进的相位延迟和幅度调制。由于动态熵取决于$\kappa(t)$的完整累积历史而非仅其瞬时值，它保留了整个蒸发过程的记忆。这些结果为研究蒸发黑洞中的时间量子关联建立了一个第一性原理动态框架。
英文摘要
Timelike entanglement entropy (tEE) has recently emerged as a novel probe of temporal quantum correlations in gravitational systems. Existing studies are largely restricted to static backgrounds. In this work we extend the construction of tEE to an evaporating Schwarzschild--AdS black hole. The evaporation is modeled through an effective Stefan--Boltzmann description of Hawking radiation coupled to an external absorptive bath, yielding a time-dependent horizon radius ($r_h(t)$) and surface gravity $κ(t)$. We derive, from the near-horizon Rindler structure of the evolving horizon, an adiabatic generalization of the static Kruskal construction, obtaining the accumulated thermal phase $Φ(t)=\int_0^tκ(t')\,dt'$ as the natural replacement for the static phase $κt$. The validity of this construction is governed by an explicit adiabatic parameter $\mathcal A(t)$, which we verify numerically remains small ($\lesssim0.012$) throughout the regime of interest. It vanishes exactly where the horizon crosses the critical radius $r_h=l/\sqrt3$ identified independently from the static thermodynamics. Using $Φ(t)$, we construct a dynamical timelike entanglement entropy that continuously tracks the evaporation process and derive the corresponding dynamical Page-like times. Unlike the uniformly spaced Page-like times of the static geometry, evaporation induces non-uniform temporal spacing, together with a progressive phase delay and amplitude modulation of the oscillatory tEE. Because the dynamical entropy depends on the full accumulated history of $κ(t)$ rather than its instantaneous value alone, it retains a memory of the entire evaporation process. These results establish a first-principles dynamical framework for investigating temporal quantum correlations in evaporating black holes.
