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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 4384093, 40 pages
https://doi.org/10.1155/2017/4384093
Research Article

Geometrical/Physical Interpretation of the Conserved Quantities Corresponding to Noether Symmetries of Plane Symmetric Space-Times

1School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, Pakistan
2Departamento de Matemáticas, Facultad de Ciencias, Pontificia Universidad Javeriana, Cra. 7 N. 40-62, Bogotá, Colombia

Correspondence should be addressed to Bismah Jamil; moc.liamg@limaj.hamsib

Received 23 February 2017; Revised 26 April 2017; Accepted 21 May 2017; Published 30 August 2017

Academic Editor: Igor L. Freire

Copyright © 2017 Bismah Jamil et al. 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 aim of this paper is to give the geometrical/physical interpretation of the conserved quantities corresponding to each Noether symmetry of the geodetic Lagrangian of plane symmetric space-times. For this purpose, we present a complete list of plane symmetric nonstatic space-times along with the generators of all Noether symmetries of the geodetic Lagrangian. Additionally, the structure constants of the associated Lie algebras, the Riemann curvature tensors, and the energy-momentum tensors are obtained for each case. It is worth mentioning that the list contains all classes of solutions that have been obtained earlier during the classification of plane symmetric space-times by isometries and homotheties.