Concircular vector fields and the Ricci solitons for the LRS Bianchi type-V spacetimes

Abstract

The purpose of this paper is to explore concircular vector fields (CVFs) of locally rotationally symmetric (LRS) Bianchi type-V spacetimes and to investigate whether these CVFs are Ricci soliton vector fields. We first obtained the concircular equations and then solved them by integrating directly. The existence of concircular symmetry imposes restrictions on the metric functions. It is shown that Bianchi type-V spacetimes admit four-, five-, six-, seven-, eight- or fifteen-dimensional CVFs. Further, we studied the Ricci soliton vector fields for all the cases where Bianchi type-V spacetimes admit CVFs. For this purpose, the obtained CVFs are substituted into Ricci soliton equations. These equations imposed further restrictions on metric functions and it is shown in each case that either all or some CVFs are also Ricci soliton vector fields. The gradient of Ricci soliton vector fields are also obtained. It is shown that the metrics that admit CVFs represent physically plausible perfect fluid models under certain conditions.