Singularity-free Bianchi spaces with nonlinear electrodynamics

TL;DR

This paper investigates the conditions under which certain anisotropic, homogeneous universes with nonlinear electromagnetic fields are free of singularities, revealing that some models are geodesically complete depending on curvature and topology.

Contribution

It demonstrates that nonlinear electromagnetic fields can lead to singularity-free Bianchi universes, extending understanding of conditions for geodesic completeness in these models.

Findings

Some Bianchi spaces with nonlinear electrodynamics are geodesically complete.

Completeness depends on space curvature and topology.

Linear Maxwell fields also produce singularity-free spacetimes under certain conditions.

Abstract

In this paper we present an analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions G$_3$. For these models we study geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete, like G$_3$IX and G$_3$VIII; however, completeness depends on the curvature of the space. When certain topology is assumed, Bianchi G$_3$IX presents geodesics that are imprisoned. It is surprising that in the linear limit (Maxwell field) the spacetimes are singularity-free even if the curvature parameter is zero.