Self-similar static solutions admitting a two-space of constant curvature

TL;DR

This paper reviews and extends recent findings on self-similar static solutions in space-times, presenting a family of metrics that include all static spherically symmetric perfect fluid solutions with homothety.

Contribution

It introduces a comprehensive family of metrics for static spherically symmetric perfect fluids admitting homothety, expanding previous results in self-similar space-times.

Findings

Includes all static spherically symmetric perfect fluid solutions with homothety.

Extends previous work by Haggag and Hajj-Boutros.

Provides a unified family of metrics for these solutions.

Abstract

A recent result by Haggag and Hajj-Boutros is reviewed within the framework of self-similar space-times, extending, in some sense, their results and presenting a family of metrics consisting of all the static spherically symmetric perfect fluid solutions admitting a homothety.