Conformal motions of locally rotationally symmetric Bianchi type I space–times in f(Q) gravity

Abstract

In this paper, first, we find locally rotationally symmetric (LRS) Bianchi type I solutions in symmetric teleparallel gravity, which is so-called f(Q) gravity, where f(Q) is the function of non-metricity scalar Q. To explore the solutions, we assume both linear as well as nonlinear f(Q) gravity models, along with some additional constraints on the components of the spacetimes. We came across twelve distinct classes of solutions for the said f(Q) gravity models. We also classify the extracted solutions according to their conformal vector fields (CVFs). The CVFs, being a generalization of the Killing vector fields (KVFs), also inherit some conservation laws. We observe the conservation of (linear, angular, or generalized) momentum, which consequently allows us to solve dynamical systems by conserved momenta. We also note the existence of proper CVFs in four cases (conformally non-flat), leaving the remaining classes of solutions to admit either homothetic vector fields (HVFs) or the KVFs. The overall dimension of CVFs for the obtained classes of solutions in f(Q) gravity is either four, five, six, or fifteen. In order to model the dynamics of extracted solutions, we find the energy density and pressure of fluid elements in each case.

Keywords

• Conformal motions
• LRS Bianchi type I solutions
• f(Q) gravity