Dilatonic (Anti-)de Sitter Black Holes and Weak Gravity Conjecture

TL;DR

This paper explores the properties of dilatonic (Anti-)de Sitter black holes, analyzing horizon conditions, interaction nature, and implications for the Weak Gravity Conjecture within Einstein-Maxwell-dilaton theory.

Contribution

It provides a detailed analysis of horizon conditions, interaction behaviors, and potential modifications to the Weak Gravity Conjecture in the context of dilatonic (Anti-)de Sitter black holes.

Findings

Identification of a critical dilaton coupling separating black hole types.

Extremal solutions are not reached for de Sitter and small dilaton coupling.

Discussion of attractive/repulsive interactions and conjecture modifications.

Abstract

Einstein-Maxwell-dilaton theory with non-trivial dilaton potential is known to admit asymptotically flat and (Anti-)de Sitter charged black hole solutions. We investigate the conditions for the presence of horizons as function of the parameters mass $M$, charge $Q$ and dilaton coupling strength $\alpha$. We observe that there is a value of $\alpha$ which separate two regions, one where the black hole is Reissner-Nordstr\"om-like from a region where it is Schwarzschild-like. We find that for de Sitter and small non-vanishing $\alpha$, the extremal case is not reached by the solution. We also discuss the attractive or repulsive nature of the leading long distance interaction between two such black holes, or a test particle and one black hole, from a world-line effective field theory point of view. Finally, we discuss possible modifications of the Weak Gravity Conjecture in the presence of both a dilatonic coupling and a cosmological constant.