Proof of the (local) angular momemtum-mass inequality for axisymmetric black holes

Abstract

We prove that for any vacuum, maximal, asymptotically flat, axisymmetric initial data for Einstein equations close to extreme Kerr data, the inequality $\sqrt{J}\le m$ is satisfied, where $m$ and $J$ are the total mass and angular momentum of the data. The proof consists in showing that extreme Kerr is a local minimum of the mass.

14 pages

References in corpus (5)

• The Dynamics of General Relativity
• The Positive Mass and Isoperimetric Inequalities for Axisymmetric Black Holes in four and five dimensions
• Proof of the (local) angular momemtum-mass inequality for axisymmetric black holes
• A variational principle for stationary, axisymmetric solutions of Einstein's equations
• Rough Solutions of the Einstein Constraint Equations

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• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
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• A Dain Inequality with charge
• The inequality between mass and angular momentum for axially symmetric black holes
• Extreme throat initial data set and horizon area--angular momentum inequality for axisymmetric black holes
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Geometric inequalities for black holes
• Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes
• On the linear stability of the extreme Kerr black hole under axially symmetric perturbations
• Horizon area--angular momentum inequality for a class of axially symmetric black holes
• Small deformations of extreme Kerr black hole initial data
• The Yamabe invariant for axially symmetric two Kerr black holes initial data
• Mass angular momentum and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity
• On a mass functional for initial data in 4+1 dimensional spacetime
• Small deformations of extreme five dimensional Myers-Perry black hole initial data
• Proof of the local mass-angular momenta inequality for $U(1{)}^2$ invariant black holes
• Angular momentum-mass inequality for axisymmetric black holes
• Bounds for axially symmetric linear perturbations for the extreme Kerr black hole
• Geometric inequalities in spherically symmetric spacetimes