Exterior Differential System for Cosmological G2 Perfect Fluids and Geodesic Completeness

TL;DR

This paper introduces a new exterior differential system formalism for G2 perfect-fluid spacetimes, simplifying Einstein equations and providing conditions for geodesic completeness, exemplified by a singularity-free metric.

Contribution

It develops a novel exterior differential system approach for G2 perfect-fluid spacetimes, enabling simplified analysis and new criteria for geodesic completeness.

Findings

Re-derivation of a singularity-free metric using the new formalism

Provision of a sufficient condition for geodesic completeness of diagonal metrics

Demonstration of the formalism's applicability to Einstein equations

Abstract

In this paper a new formalism based on exterior differential systems is derived for perfect-fluid spacetimes endowed with an abelian orthogonally transitive G2 group of motions acting on spacelike surfaces. This formulation allows simplifications of Einstein equations and it can be applied for different purposes. As an example a singularity-free metric is rederived in this framework. A sufficient condition for a diagonal metric to be geodesically complete is also provided.