Hyperbolic Ricci solitons on perfect fluid spacetimes

Abstract

In the present paper, we investigate perfect fluid spacetimes and perfect fluid generalized Roberston-Walker spacetimes that contain a torse-forming vector field satisfying almost hyperbolic Ricci solitons. We show that the perfect fluid spacetimes that contain a torse-forming vector field satisfy an almost hyperbolic Ricci soliton, and we prove that a perfect fluid generalized Roberston-Walker spacetime satisfying an almost hyperbolic Ricci soliton $ (g, \zeta, \varrho, \mu) $ is an Einstein manifold. Also, we study an almost hyperbolic Ricci soliton $ (g, V, \varrho, \mu) $ on these spacetimes when $ V $ is a conformal vector field, a torse-forming vector field, or a Ricci bi-conformal vector field.

Keywords

• perfect fluid spacetimes
• hyperbolic ricci solitons
• einstein manifolds