Spatially self-similar locally rotationally symmetric perfect fluid models

TL;DR

This paper analyzes Einstein's field equations for specific symmetric perfect fluid models by transforming them into a simplified autonomous system, studying their singularities and qualitative behavior.

Contribution

It reformulates Einstein's equations for these models into a reduced autonomous system and analyzes their singularities and qualitative dynamics.

Findings

Identification of singularity types in the models

Qualitative analysis of the autonomous system behavior

Reduction of equations for easier analysis

Abstract

Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of differential equations is reduced as far as possible. The system is subsequently analyzed qualitatively for some of the models. The nature of the singularities occurring in the models is discussed.