Solitons and geometrical structures in a perfect fluid spacetime

Abstract

Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and $\eta$-Ricci and $\eta$-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady, expanding or shrinking are also given. In a particular case when the potential vector field $\xi$ of the soliton is of gradient type, $\xi :=grad\left(f\right)$, we derive a Poisson equation from the soliton equation.