https://doi.org/10.1140/epjp/s13360-023-04175-y
Regular Article
A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity
1
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtoonkhwa, Pakistan
2
Department of Mathematics, Faculty of Science, King Abdulaziz University, PO Box 80203, 21589, Jeddah, Saudi Arabia
3
Mathematics Department, Faculty of Science, Al-Azhar University, 11884, Nasr City, Cairo, Egypt
4
School of Mathematics and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, University of the Witwatersrand, 2050, Johannesburg, South Africa
Received:
6
March
2023
Accepted:
6
June
2023
Published online:
15
June
2023
The purpose of this study is to categorize static plane symmetric perfect fluid spacetimes via concircular vector fields (CCVFs) in f(T) gravity. In order to achieve our goal we first obtained Einstein field equations (EFEs) for perfect fluid static plane symmetric spacetimes in f(T) theory of gravity and then obtained the concircular vector field equations. All these equations are solved simultaneously to obtain the components of the CCVFs and particular form of the metric functions along with conformal factors. Different possibilities are generated, which are solved completely as different cases. It turns out that perfect fluid static plane symmetric spacetimes in f(T) gravity admit CCVFs of 4, 5, 6, 7, 8 and 
dimensions. In some cases we obtained solutions of the field equations and their corresponding CCVFs when f(T) is a non-linear function of the torsion scalar T. The current study classifies a spacetime as per its CCVFs in a modified theory of gravity for the first time. The solutions obtained here are novel because the related functions f(T) are linear as well as non-linear functions of the torsion scalar T. In each case the energy density, fluid pressure and the torsion scalar T is also calculated. It is observed that in most of the cases the fluid pressure and energy density are related as 
which indicates that the universe represented by these spacetime metrics behave like dark energy or they can be vacuum energy. Also in some cases the pressure of the fluid and its density can be positive which shows that the rate of expansion can be slow down due to attractive gravitational effect.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
