Almost Schouten solitons and perfect fluid spacetimes

Abstract

In this study, we assume that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and innovative approach, we study almost Schouten and gradient Schouten solitons on perfect fluid spacetimes. It is demonstrated that in a perfect fluid spacetime obeying almost Schouten solitons the spacetime represents generalized Robertson-Walker spacetime. Also, we study a perfect fluid spacetime satisfying almost Schouten solitons and gradient Schouten solitons whose potential vector field is a $V$-Ric vector field. Finally, we study perfect fluid spacetimes obeying almost Schouten solitons and gradient Schouten solitons whose potential vector field is a torse-forming vector field.