Homotheties of a Class of Spherically Symmetric Space-Times Admitting $G_3$ as Maximal Isometry Group

TL;DR

This paper classifies and finds homothety vectors for spherically symmetric spacetimes with a maximal isometry group of G_3, expanding understanding of their geometric and physical properties without restrictions on the stress-energy tensor.

Contribution

It provides explicit metrics and homothety vectors for G_3 symmetric spacetimes, including cases with additional constraints and separable differential equations.

Findings

Metrics and homothety vectors are explicitly derived.

Includes examples illustrating the solutions.

Analyzes stress-energy tensors associated with the metrics.

Abstract

The homotheties of spherically symmetric spacetimes admitting $G_4$ , $G_6$ and $G_{10}$ as maximal isometry groups are already known, whereas for the space-times admitting $G_3$ as isometry groups, the solution in the form of differential constraints on metric coefficients requires further classification. For a class of spherically symmetric space-times admitting $G_3$ as maximal isometry groups without imposing any restriction on the stress-energy tensor, the metrics along with their corresponding homotheties are found. For the one case the metric is found along with its homothety vector that satisfies an additional constraint and is illustrated with the help of an example of a metric. For another case the metric and the corresponding homothety vector are found for a subclass of spherically symmetric space-times for which the differential constraint is reduced to separable form. Stress-energy tensor and related quantities of the metrics found are given in the relevant section.