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

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.

9 pages incl references: v2 typos corrected, few refs added: v3 few paragraphs added, version to be published in Class.Quant.Grav

References in corpus (6)

• The Swampland: Introduction and Review
• The String Landscape and the Swampland
• Euclidean Wormholes in String Theory
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Universal BPS structure of stationary supergravity solutions
• Erice Lectures on Black Holes and Attractors

Cited by in corpus (3)

• The Weak Gravity Conjecture: A Review
• Axion wormholes with massive dilaton
• Long-Range Forces Between Non-Identical Black Holes With Non-BPS Extremal Limits