The Black Hole Entropy Distance Conjecture and Black Hole Evaporation

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.

The FL bound and its phenomenological implications

“…The WGC implies that nonsupersymmetric charged black holes must be kinematically allowed to evaporate [7] and FL comes from applying a similar principle to the Nariai solutions. Including charged matter causes evaporation of the charged Nariai solutions as analyzed in detail in [5,27]. The decay is triggered by Schwinger pair production in the near-horizon electric field, which is controlled by a rate…”

Geometric Flow Equations for the Number of Space‐Time Dimensions

“…As was briefly discussed in the introductory section, some literature [9][10][11][12] has been recently produced in the attempt of realising the Swampland Distance Conjecture [5] via geometric flow equations. The SDC was originally motivated by observing that the physics of d-dimensional effective field theories, derived by compactifying D = (d + d ′ )-dimensional superstring theory, strongly depends on the moduli defining the shape of the internal dimensions.…”

“…Looking at the distance conjecture from a slightly more general and mathematical point of view, the definition of the distance within the space of background metrics is very closely related to mathematical flow equations in general relativity, like the Ricci flow, [6][7][8] where one follows the flow of a family of metrics with respect to a certain path in field space. In fact, in a recent series of works, [9][10][11][12] we have worked out a close correspondence between the generalized distance conjecture and the geometric flow equations, showing that the fixed points of the Ricci flow with vanishing curvature are typically at infinite distance in the space of geometries that are characterized by geometric parameters like the cosmological constant. Using this observation we conjectured that in general fixed points of the Ricci flow, which are at infinite distance in the background space, are accompanied by an infinite tower of states in quantum gravity.…”

Geometric Flow of Bubbles

“…The Distance Conjecture, which first appeared in [5], states that large distances in moduli space should be accompanied by infinite towers of asymptotically massless new states. Drawing inspiration from the graviton renormalization group flow in string theory σ-models, the distance conjecture was recently specified and rephrased [6][7][8][9][10] in terms of geometric flow equations, such as Hamilton's Ricci flow [11][12][13]…”