f ( R , T ) -Gravity Model with Perfect Fluid Admitting Einstein Solitons

f ( R , T ) -gravity is a generalization of Einstein’s field equations ( E F E s ) and f ( R ) -gravity. In this research article, we demonstrate the virtues of the f ( R , T ) -gravity model with Einstein solitons ( E S ) and gradient Einstein solitons ( G E S ) . We acquire the equation of state of f ( R , T ) -gravity, provided the matter of f ( R , T ) -gravity is perfect fluid. In this series, we give a clue to determine pressure and density in radiation and phantom barrier era, respectively. It is proved that if a f ( R , T ) -gravity filled with perfect fluid admits an Einstein soliton ( g , ρ , λ ) and the Einstein soliton vector field ρ of ( g , ρ , λ ) is Killing, then the scalar curvature is constant and the Ricci tensor is proportional to the metric tensor. We also establish the Liouville’s equation in the f ( R , T ) -gravity model. Next, we prove that if a f ( R , T ) -gravity filled with perfect fluid admits a gradient Einstein soliton, then the potential function of gradient Einstein soliton satisfies Poisson equation. We also establish some physical properties of the f ( R , T ) -gravity model together with gradient Einstein soliton.