Self-Similarity in General Relativity \endtitle

TL;DR

This paper reviews various types of self-similarity in general relativity, focusing on solutions with homothetic symmetry, their classifications, mathematical approaches, and applications in astrophysics and cosmology.

Contribution

It provides a comprehensive survey of self-similar solutions in Einstein's equations, emphasizing recent classifications and their roles as asymptotic states.

Findings

Complete classification of perfect fluid spherically symmetric solutions

Discussion of self-similarity as asymptotic states in models

Survey of mathematical methods for studying self-similar solutions

Abstract

The different kinds of self-similarity in general relativity are discussed, with special emphasis on similarity of the ``first'' kind, corresponding to spacetimes admitting a homothetic vector. We then survey the various classes of self-similar solutions to Einstein's field equations and the different mathematical approaches used in studying them. We focus mainly on spatially homogenous and spherically symmetric self-similar solutions, emphasizing their possible roles as asymptotic states for more general models. Perfect fluid spherically symmetric similarity solutions have recently been completely classified, and we discuss various astrophysical and cosmological applications of such solutions. Finally we consider more general types of self-similar models.