Symmetries of locally rotationally symmetric Bianchi type V spacetime

Abstract

In this paper, we classify the metric of locally rotationally symmetric Bianchi type V spacetime through its symmetries, including Killing, homothetic and conformal vector fields. In order to find all possible Bianchi type V metrics possessing these symmetries, first we analyze the symmetry equations by an algorithm developed in Maple which restricts the metric functions to satisfy certain conditions. These conditions are then used to solve the set of symmetry equations, giving the final form of symmetry vector fields. To add some physical significance of the obtained metrics, the components of energy-moments tensor are found. It is observed that most of these metrics represent perfect fluids satisfying certain energy conditions.

Keywords

• Killing vector fields
• Homothetic vector fields
• Conformal vector fields
• Bianchi type V spacetime