Ricci soliton vector fields of spherically symmetric static spacetimes

Abstract

In this paper, we focused our attention to find Ricci solitons of spherically symmetric static spacetimes. It is shown that special classes of such spacetime metrics admit shrinking, expanding or steady Ricci solitons. It is found that the dimensions of the Ricci soliton vector fields are four, five, eight, ten or eleven. It is observed that non-Einstein metrics also exist with shrinking or expanding Ricci soliton vector fields. In all the cases, the obtained Ricci soliton vector fields are proved to be gradient and concircular potential fields.