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
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016