On Spherically Symmetric Non-Static Space-Times Admitting Homothetic Motions

TL;DR

This paper investigates spherically symmetric, non-static spacetime solutions with homothetic symmetries, presenting a new self-similar solution and analyzing its physical properties within Einstein's field equations.

Contribution

It introduces a novel self-similar solution for Einstein's equations with homothetic symmetry in a general form, expanding understanding of spherically symmetric spacetimes.

Findings

New self-similar solution found

Physical properties of the solution analyzed

Homothetic symmetry conditions classified

Abstract

Spherically symmetric solutions admitting a homothetic Killing vector field (HKVF) either orthogonal, $\eta_{\bot}$, or parallel,$\eta_{||}$, to the 4-velocity vector field, $u^a$, are studied. New self-similar solution of Einstein's field equation is found in the case when HKVF is in a general form. Some physical properties of the obtained solution are examined.