Spherically symmetric models for charged radiating stars and voids: Theoretical approach

TL;DR

This paper develops a theoretical framework for matching spherically symmetric spacetimes with charged radiating solutions, establishing conditions for physical plausibility and an upper charge limit for such bodies.

Contribution

It introduces a comprehensive method for matching spherically symmetric electromagnetic and gravitational fields with Vaidya-Reissner-Nordstrom solutions, including junction conditions and physical interpretations.

Findings

Proves generic matchings to Vaidya-Reissner-Nordstrom solutions are possible.

Establishes the non-spacelike nature of the matching hypersurface.

Derives an upper limit for the total net electric charge of spherically symmetric bodies.

Abstract

We study the matching of a general spherically symmetric spacetime with a Vaidya-Reissner-Nordstrom solution. To that end, we study the properties of spherically symmetric electromagnetic fields and develop the proper gravitational and electromagnetic junction conditions. We prove that generic spacetimes can be matched to a Vaidya-Reissner-Nordstrom solution or one of its specializations, and that these matchings have clear physical interpretations. Furthermore, the non-spacelike nature of the matching hypersurface is proved under very general hypotheses. We obtain the fundamental result that any spherically symmetric body, be it in evolution or not, has un upper limit for the total net electric charge that carries.