Deformations of Charged Axially Symmetric Initial Data and the Mass-Angular Momentum-Charge Inequality

Abstract

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass, angular momentum, and charge. This extends previous work by the authors [4] (arXiv:1401.3384), in which the role of charge was omitted. Lastly, we improve upon the hypotheses required for the mass-angular momentum-charge inequality in the maximal case.

34 pages; final version. This article builds on previous work of the authors (arXiv:1401.3384) by including the electromagnetic field

References in corpus (3)

• Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum
• Rigidity in the Positive Mass Theorem with Charge
• A Penrose-Like Inequality with Charge

Cited by in corpus (4)

• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
• Relating Mass to Angular Momentum and Charge in 5-Dimensional Minimal Supergravity
• Remarks on mass and angular momenta for $U(1{)}^2$-invariant initial data