<inline-formula><math display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><mi mathvariant="script">T</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Gravity Model with Perfect Fluid Admitting Einstein Solitons

Abstract

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.

Keywords

• Einstein solitons
• gradient Einstein solitons
• perfect fluid spacetime
• f ( R , T ) -gravity%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="equation"> <inline-formula> <mml:math id="mm12222"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="script">R</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="script">T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-gravity
• lorentzian manifolds