熵-几何对应作为有效非局域引力
Entropy-geometry correspondence as effective nonlocal gravity
AI总结：
该研究针对静态球对称引力建立熵-几何对应的算子形式体系，重构非局域引力相关物理量，分析源的行为并推导视界条件，支持引力 sector 的熵修正。
AI中文摘要：
我们针对静态球对称引力，建立了熵-几何对应的算子形式体系。从广义熵出发，我们重构了有效非局域形状因子、其坐标空间源、相关的累积质量分布以及最终的时空几何。该构造针对贝肯斯坦-霍金熵、雷尼熵、察利斯-西尔托熵、巴罗熵、卡尼亚达基斯熵、对数/指数修正熵以及圈量子引力（LQG）启发的熵完成。算子表示为广义熵、非局域引力修饰与尺度依赖的有效质量或牛顿耦合之间提供了直接关联。我们分析了重构源的红外和紫外行为，讨论其物理自洽性，并确定了能恢复标准史瓦西描述的极限。我们证明，广义熵通过重构的跑动牛顿耦合精确重现面积定律，即$\boldsymbol{\text{d}}S=\boldsymbol{\text{d}}A/4G_S(r_+)$，确保热力学自洽性。由于视界熵由作用量决定，这支持引力 sector 中的熵修正。我们还推导了重构视界为具有正温度的事件视界的条件。
英文摘要：
We develop an operator formulation of the entropy-geometry correspondence for static, spherically symmetric gravity. Starting from a generalized entropy, we reconstruct an effective nonlocal form factor, its coordinate-space source, the associated cumulative mass profile, and the resulting spacetime geometry. The construction is worked out for the Bekenstein-Hawking, Rényi, Tsallis-Cirto, Barrow, Kaniadakis entropies, logarithmically/exponentially corrected entropy and LQG inspired entropy. The operator representation provides a direct relation between generalized entropy, nonlocal gravitational dressing, and a scale-dependent effective mass or Newton coupling. We analyze the reconstructed sources and their infrared and ultraviolet behavior, discuss their physical consistency, and identify the limits in which the standard Schwarzschild description is recovered. We show that the generalized entropy exactly reproduces the area law with the reconstructed running Newton coupling, $\dd S=\dd A/4G_S(r_+)$, ensuring thermodynamic consistency. Since horizon entropy is determined by the action, this favors entropy corrections in the gravitational sector. We also derive the conditions for the reconstructed horizon to be an event horizon with positive temperature.
