Spatially self-similar spherically symmetric perfect-fluid models

TL;DR

This paper analyzes Einstein's field equations for self-similar spherically symmetric perfect-fluid models by reformulating them as a compact, autonomous dynamical system and studying their qualitative behavior.

Contribution

It introduces a reduced, regular phase space formulation of the equations, enabling a detailed dynamical systems analysis of these models.

Findings

Reformulation of Einstein's equations as a first-order autonomous system.

Identification of a compact, regular phase space for analysis.

Qualitative analysis of the models' dynamical behavior.

Abstract

Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems.