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.

arXiv comment9 pages incl references: v2 typos corrected, few refs added: v3 few paragraphs added, version to be published in Class.Quant.Grav

References in corpus (20)

• The String Landscape, Black Holes and Gravity as the Weakest Force
• The Swampland: Introduction and Review
• The String Landscape and the Swampland
• The Weak Gravity Conjecture and Scalar Fields
• Sharpening the Weak Gravity Conjecture with Dimensional Reduction
• Euclidean Wormholes in String Theory
• Euclidean wormholes, baby universes, and their impact on particle physics and cosmology
• Non-Supersymmetric Attractor Flow in Symmetric Spaces
• Universal BPS structure of stationary supergravity solutions
• Generating Geodesic Flows and Supergravity Solutions
• Merging the Weak Gravity and Distance Conjectures Using BPS Extremal Black Holes
• Repulsive Forces and the Weak Gravity Conjecture
• The String Landscape, the Swampland, and the Missing Corner
• Scalar Fields, Hierarchical UV/IR Mixing and The Weak Gravity Conjecture
• Erice Lectures on Black Holes and Attractors
• Baby Universes, Holography, and the Swampland
• Duality and Axionic Weak Gravity
• Euclidean axion wormholes have multiple negative modes
• The Hesse potential, the c-map and black hole solutions
• The holographic dual to supergravity instantons in $\mathrm{Ad}{\mathrm{S}}_5\times {\mathrm{S}}^5/{\mathbb{Z}}_{\mathrm{k}}$

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