Statistical conformal Killing vector fields of locally rotationally symmetric Bianchi type-I spacetime

Source abstract

In this work a study of conformal Killing vector fields has been carried out with a new perspective of statistical connection. The study is organized into three main sections. In one section we listed the generators of conformal Killing algebra of locally rotationally symmetric (LRS) Bianchi type-I spacetimes which were obtained in a previous work [Mahmood et al., Mod. Phys. Lett. A 33, 1850063 (2018)]. In the second section we constructed statistical structure over the manifolds of the obtained LRS Bianchi type-I metrics and investigated the conditions under which the obtained vector fields for these spacetime metrics remain conformal Killing vector fields. We also discussed the vanishing Lie derivative for proper conformal Killing vectors under particular affine connections. Statistical structures of LRS Bianchi type-I spacetimes have been achieved by applying the Codazzi and torsion free conditions. In the last, we deduced some conditions under which an initial connection having torsion will produce a vanishing Lie derivative for proper conformal Killing vector fields.