Inequalities Between Size and Charge for Bodies and the Existence of Black Holes Due to Concentration of Charge

TL;DR

This paper establishes a universal inequality linking the size and charge of bodies under Einstein's equations and provides conditions for black hole formation due to charge concentration.

Contribution

It introduces a new universal inequality relating size and charge, and offers a general criterion for black hole formation from charge concentration.

Findings

Charge of a body is bounded by its size under Einstein equations.

A sufficient condition for black hole formation due to charge concentration.

Discussion on the physical implications of these inequalities.

Abstract

A universal inequality that bounds the charge of a body by its size is presented, and is proven as a consequence of the Einstein equations in the context of initial data sets which satisfy an appropriate energy condition. We also present a general sufficient condition for the formation of black holes due to concentration of charge, and discuss the physical relevance of these results.