Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R, T) gravity

Abstract

In this paper, the non-static solutions for perfect fluid distribution with plane symmetry in f(R, T) gravitational theory are obtained. Firstly, using the Lie symmetries, symmetry reductions are performed for considered vector fields to reduce the number of independent variables. Then, corresponding to each reduction, exact solutions are obtained. Killing vectors lead to different conserved quantities. Therefore, we figure out the Killing vector fields corresponding to all derived solutions. The derived solutions are further studied and it is observed that all of the obtained spacetimes, at least admit to the minimal symmetry group which consists of ∂ y , ∂ z and −z∂ y + y∂ z . The obtained metrics, admit to 3, 4, 6, and 10, Killing vector fields. Conservation of linear momentum in the direction of y and z, and angular momentum along the x axis is provided by all derived solutions.