f(R,T)-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.

Notes on η‐Einstein solitons on para‐Kenmotsu manifolds

“…In this context, one notes that $$$ \eta $$$‐Einstein solitons can be viewed as a generalization of $$$ \eta $$$‐Ricci solitons. In the recent years, Einstein and $$$ \eta $$$‐Einstein solitons have been considered by several mathematicians such as [8, 13–19] and references therein.…”

Ricci solitons on anisotropic fluid spacetime in f(R, T)-gravity

“…They showed that their model represent the dark matter era for the obtained RSVFs. Siddique et al [24] worked in f (R, T)-gravity and showed that if a perfect fluid spacetime in f (R, T)-gravity admits an Einstein soliton and the corresponding RSVF is a Killing vector field, then the scalar curvature will be constant. Siddique [25] worked on perfect fluid spacetime in f (R, T) gravity.…”

“…Siddique et al [24] worked in f (R, T)-gravity and showed that if a perfect fluid spacetime in f (R, T)-gravity admits an Einstein soliton and the corresponding RSVF is a Killing vector field, then the scalar curvature will be constant. Siddique [25] worked on perfect fluid spacetime in f (R, T) gravity. The author obtained modified Poisson and Liouville equations from the Ricci soliton equation.…”

“…Our aim in this paper is to extend the work presented in [25] for the anisotropic fluid spacetime and to obtain a general condition for the radial and tangential pressures under which an anisotropic spacetime in f (R, T)gravity will admit a shrinking, expanding or steady Ricci soliton. We will also obtain a modified Poisson equation and modified Liouville equation from the Ricci soliton equation in f (R, T)-gravity filled with anisotropic fluid.…”

A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor

“…Here α, β are scalars and u k is a 1-form [12][13][14][15][16][17][18]. A perfect fluid spacetime is pictured as a Lorentzian quasi-Einstein manifold given that u k is a unit time-like vector field [14,19,20]. These manifolds emerged during the investigation of Einstein's field equation.…”