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