Weak Gravity Conjecture in de Sitter space-time

TL;DR

This paper extends the Weak Gravity Conjecture to de Sitter space, proposing a charge bound for black holes that depends on the space's curvature, with implications for quantum gravity theories.

Contribution

It introduces a generalized Weak Gravity Conjecture in de Sitter space, relating black hole charge bounds to the space's curvature and providing a new perspective on quantum gravity constraints.

Findings

Charge bound depends on de Sitter radius and mass.

In flat space limit, the bound reduces to known results.

Behavior of charge bound varies with space curvature.

Abstract

We propose a generalisation of the Weak Gravity Conjecture in de Sitter space by studying charged black-holes and comparing the gravitational and an abelian gauge forces. Using the same condition as in flat space, namely the absence of black-hole remnants, one finds that for a given mass $m$ there should be a state with a charge $q$ bigger than a minimal value $q_{\rm min}(m,l)$, depending on the mass and the de Sitter radius $l$, in Planck units. In the large radius flat space limit (large $l$), $q_{\rm min}\to m$ leading to the known result $q>m/\sqrt{2}$, while in the highly curved case (small $l$) $q_{\rm min}$ behaves as $\sqrt{ml}$. We also discuss the example of the gauged R-symmetry in $N=1$ supergravity.