发表机构
Zhejiang Normal University; Zhejiang Institute of Photoelectronics（浙江师范大学; 浙江省光电子研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文首次引入守恒的霍金尺度各向异性源，求解固定ADM质量下静态黑洞的爱因斯坦方程，得到修饰几何，并揭示其热响应伴随轨道重构，为随机引力程序奠定确定性平均场基础。
AI 中文摘要
黑洞通常被描述为量子场在其上传播的经典几何，或者被描述为其完整量子描述超越半经典引力的物体。然而，霍金辐射已经表明，黑洞并非一个完全孤立的系统：视界带有热尺度，并且在粗粒化后，可能关联着涨落、耗散和环境相关性。这种视界尺度的开放性能否在度规的随机处理之前，直接编码到引力背景中，仍然是一个悬而未决的问题。在此，我们通过首次引入一个守恒的霍金尺度各向异性源来回答这一问题，该源代表粗粒化的近视界大气，并在固定ADM质量下求解静态黑洞的爱因斯坦方程。修饰后的几何具有重整化的质量函数、自洽移动的视界和修正的表面引力。由于同一时移函数同时支配视界和类时测地线，热响应伴随着相关的轨道重构：有效势被重整化，ISCO向内移动，近视界停留时间增加。该构造没有向固定的史瓦西背景添加朗之万力；相反，它定义了一个确定性的修饰平均几何，为随后在爱因斯坦-朗之万框架中处理随机度规涨落提供了受控背景。这确立了确定性平均场部分作为未来处理视界尺度开放性的随机引力程序的必要第一步。
英文摘要
Black holes are usually described either as classical geometries on which quantum fields propagate or as objects whose complete quantum description lies beyond semiclassical gravity. Hawking radiation already shows, however, that a black hole is not an exactly isolated system: the horizon carries a thermal scale and, after coarse graining, may be associated with fluctuations, dissipation and environmental correlations. Whether this horizon-scale openness can be encoded directly in the gravitational background, before any stochastic treatment of the metric, remains an open question. Here we answer it by introducing, for the first time, a conserved Hawking-scale anisotropic source representing the coarse-grained near-horizon atmosphere and solving the Einstein equations for a static black hole at fixed ADM mass. The dressed geometry has a renormalized mass function, a self-consistently shifted horizon and a modified surface gravity. Because the same lapse governs the horizon and timelike geodesics, the thermal response is accompanied by a correlated orbital restructuring: the effective potential is renormalized, the ISCO moves inward and the near-horizon residence time increases. The construction adds no Langevin force to a fixed Schwarzschild background; rather, it defines a deterministic dressed mean geometry, providing a controlled background on which stochastic metric fluctuations may subsequently be treated in the Einstein-Langevin framework. This establishes the deterministic mean-field sector as the necessary first step for future stochastic gravity programs addressing horizon-scale openness.
Comments15 pages, 5 figures
