Timelike self-similar spherically symmetric perfect-fluid models

TL;DR

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

Contribution

It reformulates the Einstein equations into a simplified autonomous system with compact phase space for better analysis of self-similar solutions.

Findings

Reduced the field equations to a minimal autonomous system

Achieved a compact, regular phase space for analysis

Provided qualitative insights into the solution structure

Abstract

Einstein's field equations for timelike 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 using the theory of dynamical systems.