Stationary Bianchi type II perfect fluid models

TL;DR

This paper analyzes stationary Bianchi type II perfect fluid cosmological models using dynamical systems, revealing their asymptotic properties and presenting a new exact solution.

Contribution

It reformulates Einstein's equations for these models as a dynamical system and provides new insights into their asymptotic behavior and a novel exact solution.

Findings

Locally rotationally symmetric models are not asymptotically self-similar for small variables.

The phase space of the models is compactified, enabling qualitative analysis.

A new exact solution to Einstein's field equations for these models is presented.

Abstract

Einstein's field equations for stationary Bianchi type II models with a perfect fluid source are investigated. The field equations are rewritten as a system of autonomous first order differential equations. Dimensionless variables are subsequently introduced for which the reduced phase space is compact. The system is then studied qualitatively using the theory of dynamical systems. It is shown that the locally rotationally symmetric models are not asymptotically self-similar for small values of the independent , tovariable. A new exact solution is also given.