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Advances in Mathematical Physics
Volume 2018, Article ID 8195208, 8 pages
https://doi.org/10.1155/2018/8195208
Research Article

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

1Department of Mathematics, University of the Punjab, Lahore, Pakistan
2Beaconhouse School System, Gujranwala, Pakistan

Correspondence should be addressed to Daud Ahmad; kp.ude.up@htam.duad

Received 20 September 2017; Revised 27 November 2017; Accepted 28 November 2017; Published 31 January 2018

Academic Editor: Kaliyaperumal Nakkeeran

Copyright © 2018 Daud Ahmad and Kashif Habib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The homotheties of spherically symmetric space-time admitting , , and as maximal isometry groups are already known, whereas, for the space-time admitting 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 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.