Perfect fluid locally rotationally symmetric Bianchi Type-I spacetimes admitting concircular vector fields in f(T) gravity

Abstract

We obtained the solutions of Einstein’s Field Equations (EFEs) for locally rotationally symmetric (LRS) Bianchi type-I perfect fluid spacetimes through the concircular vector fields (CCVFs) in [Formula: see text] gravity. It is shown that such metrics admit CCVFs of 4, 5, 6, 7, 8 and 15 dimensions. We also calculated the energy density, fluid pressure, torsion scalar [Formula: see text] and the form of the function [Formula: see text]. We did not specify the form of [Formula: see text] for the solution of EFEs but found a particular form of [Formula: see text] during the process of finding the CCVFs. It is observed that energy density and fluid pressure of some solutions are related as [Formula: see text], which means that the universe represented by these spacetime metrics behaves like dark energy models. For other solutions, it is observed that the fluid pressure and energy density can remain positive for particular choices of the constants involved. Thus, in these cases the rate of expansion can slow down due to positive attractive effect. We also calculated the Hubble’s parameter ([Formula: see text]), scalar expansion ([Formula: see text]), shear scalar ([Formula: see text]), anisotropy parameter ([Formula: see text]) and the deceleration parameter ([Formula: see text]) associated with each of the obtained exact LRS Bianchi type-I solutions. It is observed that the physical behavior of the spacetime changes with the number of admitting CCVFs. A constant anisotropic behavior for 15-dimensional CCVFs is observed to change to isotropic nature for seven-dimensional CCVFs.