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

TL;DR

This paper extends the mass-angular momentum-charge inequality to more general axisymmetric initial data in Einstein-Maxwell theory, providing reduction techniques and improved conditions for the inequality's validity.

Contribution

It introduces a reduction method to general initial data, extending previous maximal case results to include charge and improving hypotheses for the inequality.

Findings

Reduction of general inequality to maximal case with solutions

Extension of inequality to include charge and black hole area bounds

Improved hypotheses for the validity of the 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.