Mass-Angular Momentum Inequality For Black Ring Spacetimes

Abstract

The inequality $m^3\ge \frac{27\pi }{4}|{\mathcal{J}}_2||{\mathcal{J}}_1-{\mathcal{J}}_2|$ 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.

5 pages; V2: minor improvements

References in corpus (5)

• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• An instability of higher-dimensional rotating black holes
• End Point of the Ultraspinning Instability and Violation of Cosmic Censorship
• A supersymmetric black lens
• The Black Ring is Unstable

Cited by in corpus (6)

• Late-time asymptotics for the wave equation on extremal Reissner-Nordström backgrounds
• Horizon hair of extremal black holes and measurements at null infinity
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes
• Numerical Evidence for Non-Axisymmetric Gravitational "Hair" for Extremal Kerr Black Hole Spacetimes with Hyperboloidal Foliations
• Note on the thermodynamic stability of a black ring at quantum scales