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

f(R,T)-gravity is a generalization of Einstein’s field equations (EFEs) and f(R)-gravity. In this research article, we demonstrate the virtues of the f(R,T)-gravity model with Einstein solitons (ES) and gradient Einstein solitons (GES). 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.