A comment on no-force conditions for black holes and branes

TL;DR

This paper simplifies the derivation of no-force conditions for black holes, branes, and gravitational instantons within the Weak Gravity Conjecture framework, highlighting their self-repulsive nature and implications for path integrals.

Contribution

It provides a streamlined derivation of no-force conditions using timelike reduction, extending the concept of quasi-extremality to gravitational instantons and wormholes.

Findings

Quasi-extremality relates to vanishing horizon or surface gravity.

Black holes and branes obey no-force conditions at quasi-extremality.

Macroscopic axion wormholes are self-repulsive and do not contribute to the path integral.

Abstract

In the context of the Weak Gravity Conjecture the notion of quasi-extremality for black holes and branes was recently defined as the property of having either vanishing horizon size or surface gravity. It was derived that such objects obey a no-force condition. In this short note I present a simplified derivation that is essentially present in the formalism of timelike reduction pioneered by Breitenlohner, Gibbons and Maison. This formalism also provides the natural definition of quasi-extremality for gravitational instantons (and wormholes) sourced by axion fluxes and strengthens the argument that macroscopic axion wormholes do not contribute in the path integral since they are self-repulsive in a Euclidean sense.