Inequalities Between Size, Mass, Angular Momentum, and Charge for Axisymmetric Bodies and the Formation of Trapped Surfaces

TL;DR

This paper derives inequalities linking size, mass, angular momentum, and charge for axisymmetric bodies in general relativity, providing new criteria for black hole formation applicable even without maximal conditions.

Contribution

It introduces general inequalities relating physical and geometric quantities of axisymmetric bodies, valid without maximal assumptions, and offers black hole formation criteria applicable in various cases.

Findings

Established inequalities relating size, mass, angular momentum, and charge.

Provided black hole existence criteria valid in time-symmetric and non-maximal cases.

Included effects of boundaries in the inequalities.

Abstract

We establish inequalities relating the size of a material body to its mass, angular momentum, and charge, within the context of axisymmetric initial data sets for the Einstein equations. These inequalities hold in general without the assumption of the maximal condition, and use a notion of size which is easily computable. Moreover, these results give rise to black hole existence criteria which are meaningful even in the time-symmetric case, and also include certain boundary effects.