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 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.

Newton versus Coulomb for Kaluza–Klein modes

“…where α is the dilatonic coupling of the form e 2 √ 2ακφ F 2 , exists. We have therefore recovered in this explicit amplitude computation the dilatonic weak gravity conjecture that was derived in [3] (see also [4] for its generalization) from the study of the extremal Einstein-Maxwell-dilaton black hole solutions. In the absence of the massless dilaton field α = 0, one trivially retrieves the original WGC condition…”

“…In this work we will be interested in a particular case of them. The present work is dedicated to the study of two different generalizations of the WGC: one that arises when the gauge interaction is complemented by a dilaton interaction [3,4], and another [5][6][7] that broadly requires the dominance of scalar interactions with respect to gravity in some scattering processes depending on the specific theory. We are interested in the modes that propagate in an extra dimension forming a tower of KK excitations [8][9][10][11].…”

“…In Sect. 4, we consider adding a mass term for the scalar in D +1 dimensions and we find our form of the scalar WGC. A non-minimal coupling to gravity is considered in Sect.…”

Bernstein spectral method for quasinormal modes of a generic black hole spacetime and application to instability of dilaton-de Sitter solution

“…( 32) leads to the correct expression for the compact coordinate (36). The prefactor in (33) and the equation for the regular function ψ(u) cannot be obtained by taking this limit. The reason is that the singular point u = 0 becomes irregular for the asymptotically flat spacetime.…”

“…When D = 0, the space-time reduces the Schwarzschild-de Sitter solution. Some basic properties of this black hole solution were studied in [25,33,34].…”