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 α. We observe that there is a value of α 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 α, 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.
Highlights
The present work began when we asked ourselves what happens to the de Sitter Weak Gravity Conjecture in the case of a dilatonic gauge coupling
For large values of α, the extremality condition obtained by identification of the horizon rh(= r+) with the singularity r−, would formally correspond in the Schwarzschild case to put the horizon at the origin i.e. formally take the limit M tends to 0 in the black hole solution which in turn leads to a divergent temperature
We attempt to infer from them new bounds for the Dilatonic Weak Gravity Conjecture (DWGC)
Summary
The Reissner-Nordström black holes are parametrized by their charge Qand mass M. As long as the second term in g00 (de Sitter-like) is sub-dominant, the transition between black holes and naked singularities (with a cosmological horizon) seems to happen in the same parametric region as in asymptotically flat space-time. The lower bound on this black hole region is given by (4.21) and it is represented in yellow in figure 3 It corresponds to the limit where the event horizon coincides with the singularity. The graphical representation of the two bounds reveals that for masses M > √7 the event horizon cannot form: this is the maximal mass above which asymptotically de Sitter black hole solutions are no more possible (yellow dashed line) This point corresponds to a maximal charge. Note that in all previous literature, because the asymptotically flat metric always shows a naked singularity before turning complex, this region was ignored
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