Riemann solitons on perfect fluid spacetimes

Abstract

In this article, we characterize Riemann solitons on perfect fluid spacetimes. Some relationship between perfect fluid spacetimes and Riemann solitons with certain soliton vector fields are established. We investigate Ricci-symmetric perfect fluid spacetimes whose metrics are Riemann solitons. Pseudo-projectively flat perfect fluid spacetimes with the metrics as Riemann solitons have been studied. It is also proved that a gradient Riemann soliton on a perfect fluid spacetime is Einstein. An example of a gradient Riemann soliton on perfect fluid spacetime has been constructed