Absolute Stability Limit for Relativistic Charged Spheres

TL;DR

This paper derives an exact stability limit for relativistic charged spheres with specific density distributions, providing a fundamental bound applicable to various configurations and supported by numerical analysis.

Contribution

It presents an exact solution for the stability limit of relativistic charged spheres with specific density profiles, extending understanding of their stability bounds.

Findings

Exact stability limit derived for constant density spheres

Cruder bounds established for general density distributions

Numerical results illustrating stability conditions

Abstract

We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. We then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. We give numerical results for all cases. In addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell.