Horizon area--angular momentum inequality for a class of axially symmetric black holes

Abstract

We prove an inequality between horizon area and angular momentum for a class of axially symmetric black holes. This class includes initial conditions with an isometry which leaves fixed a two-surface. These initial conditions have been extensively used in the numerical evolution of rotating black holes. They can describe highly distorted black holes, not necessarily near equilibrium. We also prove the inequality on extreme throat initial data, extending previous results.

23 pages, 5 figures. We improved the hypothesis of the main theorem

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• Black hole Area-Angular momentum inequality in non-vacuum spacetimes
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Black hole Area-Angular momentum-Charge inequality in dynamical non-vacuum spacetimes
• Area-angular momentum-charge inequality for stable marginally outer trapped surfaces in 4D Einstein-Maxwell-dilaton theory
• On the shape of rotating black-holes
• Four types of attractive gravity probe surfaces
• Refined inequalities for loosely trapped surface/attractive gravity probe surface
• Mass angular momentum and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity
• Axially symmetric spacetimes: numerical and analytical perspectives
• Avenues for Analytic exploration in Axisymmetric Spacetimes. Foundations and the Triad Formalism