Homogeneous solutions to the Einstein-matter equations with a magnetic field and a conformal gauge singularity

TL;DR

This paper investigates homogeneous solutions to Einstein's equations with magnetic fields and matter models, revealing the existence and uniqueness of solutions in certain kinetic theory cases and their behavior near singularities.

Contribution

It provides the first analysis of massless Einstein-matter solutions with magnetic fields and conformal singularities, especially for kinetic matter models.

Findings

No solutions for radiation fluid matter model.

Unique solutions exist for Einstein-Vlasov and Einstein-Boltzmann systems with soft potentials.

Asymptotic expansions near the conformal gauge singularity are derived.

Abstract

We study massless solutions to the Einstein equations coupled to different matter models with a magnetic field and a conformal gauge singularity assuming spatial homogeneity with three commuting spatial translations. We show that there are no solutions in the case that the matter model is a radiation fluid. If the matter is described via kinetic theory we obtain that there exist unique solutions to the Einstein-Vlasov system and the Einstein-Boltzmann system for a certain range of soft potentials. For both the Vlasov and the Boltzmann case we also obtain asymptotic expansions close to the initial conformal gauge singularity.