近极值正则黑洞的纠缠岛与信息恢复
Entanglement islands and information recovery from near-extremal regular black holes
AI总结：
本研究针对受T对偶启发的近极值正则黑洞，通过岛处方计算辐射广义熵，结合修正后的引力熵得到佩奇曲线，证实需纳入量子修正以实现信息恢复的热力学自洽描述。
AI中文摘要：
我们研究了受T对偶启发的近极值正则黑洞中的佩奇（Page）曲线与信息恢复，这类黑洞的中心奇点由最小长度尺度解决。通过在固定最小长度下积分热力学第一定律，我们得到了包含固有量子对数修正的黑洞熵，而面积律贡献在极值极限下消失。因此，极值残余携带有限的纯量子起源熵。利用近视界区域的岛（island）处方，我们计算了辐射的广义熵，并将标准面积泛函与由修正后的黑洞热力学熵构造的替代泛函进行比较。在近极值极限下，后者解析地简化为带有有效耦合的经典极值问题，且使物理岛更靠近外视界。尽管两种处方均产生佩奇转变，但它们预测了不同的饱和值与佩奇时间：标准泛函产生由面积项控制的平台，而修正后的处方饱和于外视界的完整热力学熵，在极值极限下则饱和于对数形式的残余熵。纳入蒸发与反作用后，佩奇曲线呈现出预期的下降分支，并渐近于冷极值残余的熵而非零。我们的结果表明，对正则近极值黑洞的信息恢复进行热力学自洽描述，需要纳入引力熵的固有量子修正。
英文摘要：
We investigate the Page curve and information recovery in a near-extremal regular black hole inspired by T-duality, in which the central singularity is resolved by a minimal length scale. By integrating the first law of thermodynamics at fixed minimal length, we obtain a black-hole entropy containing an intrinsically quantum logarithmic correction, while the area-law contribution vanishes in the extremal limit. Consequently, the extremal remnant carries a finite entropy of purely quantum origin. Using the island prescription in the near-horizon regime, we evaluate the generalized entropy of radiation and compare the standard area functional with an alternative functional constructed from the corrected thermodynamic entropy of the black hole. In the near-extremal limit, the latter reduces analytically to the classical extremization problem with an effective coupling, and it places the physical island closer to the outer horizon. Although both prescriptions produce a Page transition, they predict different saturation values and Page times. While the standard functional yields a plateau controlled by the area term, the corrected prescription saturates at the full thermodynamic entropy of the outer horizon and, in the extremal limit, at the logarithmic remnant entropy. Including evaporation and backreaction, the Page curve develops the expected descending branch and asymptotes to the entropy of the cold extremal remnant rather than to zero. Our results indicate that a thermodynamically consistent description of information recovery from regular near-extremal black holes requires incorporating the intrinsic quantum correction to the gravitational entropy.
