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A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

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Abstract

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 \(15-\)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 \(p\,=\,-\rho \) 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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I hereby certify that data presented in this manuscript is our own and original. All the calculations have done by us and no data is taken from other sources or published materials except where citation is made. This is a mathematical work and we can provide the proofs at any instant if required.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtoonkhwa, Pakistan

    Syed Majid Shah & Suhail Khan

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, PO Box 80203, Jeddah, 21589, Saudi Arabia

    Ahmad Tawfik Ali

  3. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, 11884, Egypt

    Ahmad Tawfik Ali

  4. School of Mathematics and DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, University of the Witwatersrand, Johannesburg, 2050, South Africa

    Sameerah Jamal

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  1. Syed Majid Shah
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Correspondence to Suhail Khan.

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Shah, S.M., Khan, S., Ali, A.T. et al. A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity. Eur. Phys. J. Plus 138, 533 (2023). https://doi.org/10.1140/epjp/s13360-023-04175-y

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