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, $\xi :=grad(f)$, we derive a Poisson equation from the soliton equation.

19 pages

References in corpus (1)

• $\eta$-Ricci solitons in $(\epsilon )$-almost paracontact metric manifolds

Cited by in corpus (4)

• Perfect fluid spacetimes and gradient solitons
• Characterizations of Perfect fluid spacetimes obeying $f(\mathcal{R})$-gravity equipped with different gradient solitons
• Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime
• Ricci Soliton and Geometrical Structure in a Perfect Fluid Spacetime with Torse-forming Vector Field