Eur. Phys. J. Plus (2016) 131: 115
https://doi.org/10.1140/epjp/i2016-16115-6

Regular Article

Concircular vector fields for plane-symmetric static spacetimes

¹ King Abdulaziz University, Faculty of Science, Department of Mathematics, PO Box 80203, 21589, Jeddah, Saudi Arabia
² Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt
³ Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtoonkhwa, Pakistan

^* e-mail: ahmadtawfik95@gmail.com

Received: 22 December 2015
Revised: 13 February 2016
Accepted: 1 March 2016
Published online: 22 April 2016

Abstract

In this paper, we investigate concircular vector fields (CVFs) of static plane symmetric four-dimensional Lorentzian manifold. Ten conformal Killing equations and their general form of conformal Killing vector fields (CKVFs) are derived along with their conformal factor. These CKVFs are then placed into the conformal Ricci collineation equations to obtain the final form of CVFs. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that plane-symmetric static spacetimes admit four, six, seven or fifteen-dimensional concircular vector fields. Analysis of our results are also given in the light of some established results in the literature.