Relativistic Charged Spheres II: Regularity and Stability

TL;DR

This paper explores the existence, regularity, and stability of static, charged fluid spheres in general relativity, generalizing previous solutions and identifying stable configurations that could model charged particles.

Contribution

It extends known solutions of Einstein's equations to include varied charge distributions and demonstrates the stability of certain configurations, challenging previous conjectures.

Findings

Existence of regular, charged fluid sphere solutions with varied charge distributions.

Identification of stable solutions against radial perturbations.

Refutation of a previous conjecture regarding these configurations.

Abstract

We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by exact solutions of Einstein's field equations. A family of these solutions had already be found (de Felice et al., 1995) but here we generalize that result to cases with different charge distribution within the spheres and show, in an appropriate parameter space, that the set of such physically reasonable solutions has a non zero measure. We also perform a perturbation analysis and identify the solutions which are stable against adiabatic radial perturbations. We then suggest that the stable configurations can be considered as classic models of charged particles. Finally our results are used to show that a conjecture of Kristiansson et al. (1998) is incorrect.