The Angular Tension of Black Holes

TL;DR

This paper introduces angular tension as a new ADM charge affecting black hole thermodynamics, providing insights into black hole phase structure and resolving degeneracies among different black hole solutions.

Contribution

It defines angular tension as an ADM charge, derives a new Smarr formula, and demonstrates its role in black hole phase diagrams and solution classification.

Findings

Angular tension contributes to the first law of black hole mechanics.

It resolves degeneracies between spherical black holes and black rings.

It captures the physics of black ring balance conditions.

Abstract

Angular tension is an ADM charge that contributes a work term to the first law of black hole mechanics when the range of an angular coordinate is varied and leads to a new Smarr formula for stationary black holes. A phase diagram for singly-spinning D=5 black holes shows that angular tension resolves the degeneracies between spherical black holes and (dipole) black rings and captures the physics of the black ring balance condition. Angular tension depends on the behavior of the metric at rotational axes and we speculate on its relation to rod/domain structure characterizations of higher dimensional black holes and black hole uniqueness theorems.