Homotheties of a Class of Spherically Symmetric Space-Time Admitting G3 as Maximal Isometry Group

Abstract

The homotheties of spherically symmetric space-time admitting G4, G6, and G10 as maximal isometry groups are already known, whereas, for the space-time admitting G3 as isometry groups, the solution in the form of differential constraints on metric coefficients requires further classification. For a class of spherically symmetric space-time admitting G3 as maximal isometry groups without imposing any restriction on the stress-energy tensor, the metrics along with their corresponding homotheties are found. In 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. In another case, the metric and the corresponding homothety vector are found for a subclass of spherically symmetric space-time 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.