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

Mohd Danish Siddiqi, Sudhakar K. Chaubey and Mohammad Nazrul Islam Khan
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Mohd Danish Siddiqi: Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
Sudhakar K. Chaubey: Section of Mathematics, Department of IT, University of Technology and Applied Sciences-Shinas, Shinas 324, Oman
Mohammad Nazrul Islam Khan: Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2021, vol. 10, issue 1, 1-13

Abstract: 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.

Keywords: Einstein solitons; gradient Einstein solitons; perfect fluid spacetime; f ( R , T ) -gravity; lorentzian manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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