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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. The recently proposed Black Hole Entropy Distance Conjecture are extended 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, the authors 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, the evaporation of these black holes is studied and related to the geometric distance. It is found that the corresponding distance to the final stage of evaporation is finite. This leads to the conclusion that evaporation does not lead to the appearance of a light tower of black hole microstates. [ABSTRACT FROM AUTHOR]

Abstract: We consider a particular set of ghost‐free interactions for three spin‐2 fields in which we freeze out the dynamics of the metric tensor that couples to the matter sector. Integrating out the non‐dynamical degrees of freedom in vacuum results in a ghost‐free bimetric theory. In the presence of the matter source, which we treat as a small perturbation, the equations for the non‐dynamical field can be solved perturbatively for its vierbein. This results in ghost‐free bimetric theory in vierbein formulation with a modified matter coupling. To lowest order in matter perturbations, we precisely obtain an effective matter coupling that has been suggested earlier in the literature. This coupling contains a linear combination of the two vierbeine whose corresponding metric fluctuation coincides with the massless spin‐2 mode. In the past, bimetric theory with this symmetric coupling has been treated as an effective theory valid at low energies without a ghost‐free completion. Our results demonstrate that the effective matter coupling can be rendered entirely ghost‐free by including the higher‐order corrections obtained from the trimetric setup. [ABSTRACT FROM AUTHOR]