The Black Hole Entropy Distance Conjecture and Black Hole Evaporation

TL;DR

This paper extends the Black Hole Entropy Distance Conjecture to charged black holes in de Sitter space, relating geometric distances to entropy and analyzing black hole evaporation's impact on microstate towers.

Contribution

It generalizes the conjecture to charged black holes in de Sitter space and links geometric distances to entropy, providing insights into black hole evaporation and microstate emergence.

Findings

Distance relates to the logarithm of entropy

Infinite entropy limit predicts a massless tower of modes

Evaporation reaches a finite distance, not producing light microstates

Abstract

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.