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.

arXiv comment5 pages; V2: minor improvements

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Cited by in corpus (6)

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• 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