We extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evaporation is finite. We conclude that evaporation does not lead to the appearance of a light tower of black hole microstates.

中文翻译：

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黑洞熵距离猜想和黑洞蒸发

我们将最近提出的黑洞熵距离猜想扩展到de Sitter空间中带电黑洞的情况。通过系统地研究具有多个视界的黑洞几何空间中的距离，我们发现该距离通常与熵的对数相关。根据无限距离的猜想，这可以预测无限熵模态下无质量模态塔的出现。此外，我们研究了这些黑洞的蒸发并将其与几何距离相关联。我们发现到蒸发最后阶段的相应距离是有限的。我们得出结论，蒸发不会导致出现黑洞微态灯塔。