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

Mohd Danish Siddiqi,Sudhakar K Chaubey,Mohammad Nazrul Islam Khan

doi:10.3390/math10010082

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.

Highlights

The general theory of relativity (GR) says that the gravitation is a geometric property as symmetric curvature of spacetime
The physical matter symmetry is specially relating to the spacetime geometry
An important symmetry is a soliton that connects to geometrical flow of spacetime geometry

Summary

Introduction

The general theory of relativity (GR) says that the gravitation is a geometric property as symmetric curvature of spacetime. The physical matter symmetry is specially relating to the spacetime geometry. The space time symmetries are used in the study of exact solutions of Einstein’s field equations of general relativity. An important symmetry is a soliton that connects to geometrical flow of spacetime geometry. Hamilton suggested to use the evolution equation, known as Ricci flow, in order to establish Thurston’s geometrization hypothesis in a three-dimensional manifold. In 1982, he [1] proposed the idea of the Ricci soliton (RS) on a Riemannian manifold M and noted that it moves under the. Via diffeomorphism of the initial metric, where g, Ric and t indicate the Riemannian metric, Ricci tensor and time, respectively. An RS (g, V, λ) on M takes the form

Ric λg

EOS is ω

These relations together with

The last two equations infer that