Gravitational collapse of plasmas in General Relativity

TL;DR

This paper develops a covariant framework for analyzing plasma collapse under gravity in general relativity, simplifying the description of spherically symmetric collapse and connecting it to known spacetime solutions.

Contribution

It introduces a covariant derivation of plasma physics in curved spacetime and simplifies the analysis of gravitational collapse by reducing to a single coordinate system.

Findings

Unified description of collapsing plasmas in a single coordinate system

Connection to charged Vaidya spacetime for exterior regions

Simplification of junction conditions in spherical symmetry

Abstract

We provide a covariant derivation of plasma physics coupled to gravitation by utilizing the 3+1 formulation of general relativity, including a discussion of the Lorentz force law. We then reduce the system to the spherically symmetric case and show that all regions of the spacetime can be represented in a single coordinate system, thus revoking the need for junction conditions. We further show that the region exterior to the collapsing region is naturally described by the charged Vaidya spacetime in non-null coordinates.