Kinematic self-similar locally rotationally symmetric models

TL;DR

This paper explores kinematic self-similarity in locally rotationally symmetric models within general relativity, providing explicit metric forms and solutions for perfect fluid models with maximal symmetry.

Contribution

It offers a comprehensive analysis of kinematic self-similar solutions in locally rotationally symmetric spacetimes, including explicit metric expressions and classification of homothetic perfect fluid solutions.

Findings

Explicit metric forms for self-similar models are derived.

All homothetic perfect fluid solutions with maximal symmetry are classified.

Coordinate expressions for the self-similar vectors are provided.

Abstract

A brief summary of results on kinematic self-similarities in general relativity is given. Attention is focussed on locally rotationally symmetric models admitting kinematic self-similar vectors. Coordinate expressions for the metric and the kinematic self-similar vector are provided. Einstein's field equations for perfect fluid models are investigated and all the homothetic perfect fluid solutions admitting a maximal four-parameter group of isometries are given.