# Mass-Angular Momentum Inequality For Black Ring Spacetimes

## TL;DR

This paper proves a sharp mass-angular momentum inequality for black ring spacetimes, linking total mass and angular momenta, with implications for black ring stability and gravitational collapse.

## Contribution

It establishes a new inequality for black rings, showing it is saturated by extreme solutions, and discusses its physical significance and relation to black ring instability.

## Key findings

- Inequality is sharp and saturated by extreme black rings.
- Provides evidence relating to black ring instability.
- Connects inequality to gravitational collapse scenarios.

## Abstract

The inequality $m^3\geq \frac{27\pi}{4} |\mathcal{J}_{2}||\mathcal{J}_{1}-\mathcal{J}_{2}|$ relating total mass and angular momenta, is established for (possibly dynamical) spacetimes admitting black holes of ring ($S^1\times S^2$) topology. This inequality is shown to be sharp in the sense that it is saturated precisely for the extreme Pomeransky-Sen'kov black ring solutions. The physical significance of this inequality and its relation to new evidence of black ring instability, as well as the standard picture of gravitational collapse, are discussed.