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

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-Nordström-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.

40 pages, 6 figures. Matches the published version: one typo corrected and one paragraph added for clarifications

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• Bianchi IX geometry and the Einstein-Maxwell theory
• Electric and dilatonic fields of a charged massive particle at rest in the field of a charged dilaton black hole
• Quasibound states of massive charged scalars around dilaton black holes in $2+1$ dimensions: Exact frequencies
• Reissner-Nordström black holes in de Sitter space-time: bounds with quasinormal frequencies