Homothetic perfect fluid space-times

TL;DR

This paper explores homothetic symmetries in General Relativity, classifies associated Lie algebra structures, and introduces new perfect fluid solutions in inhomogeneous space-times with specific homothetic groups.

Contribution

It provides a comprehensive classification of homothetic Lie algebras in inhomogeneous space-times and presents new perfect fluid solutions with detailed metric and vector expressions.

Findings

Classification of Lie algebra structures for homothetic groups

New perfect fluid solutions with explicit metrics

Analysis of inhomogeneous models with $H_4$ and $H_3$ groups

Abstract

A brief summary of results on homotheties in General Relativity is given, including general information about space-times admitting an r-parameter group of homothetic transformations for r>2, as well as some specific results on perfect fluids. Attention is then focussed on inhomogeneous models, in particular on those with a homothetic group $H_4$ (acting multiply transitively) and $H_3$. A classification of all possible Lie algebra structures along with (local) coordinate expressions for the metric and homothetic vectors is then provided (irrespectively of the matter content), and some new perfect fluid solutions are given and briefly discussed.