Study of Decoupled Anisotropic Solutions in f(R, T, RρηTρη) Theory

Tayyab Naseer,Muhammad Sharif

doi:10.3390/universe8020062

Abstract

In this paper, we consider isotropic solution and extend it to two different exact well-behaved spherical anisotropic solutions through minimal geometric deformation method in f(R,T,RρηTρη) gravity. We only deform the radial metric component that separates the field equations into two sets corresponding to their original sources. The first set corresponds to perfect matter distribution while the other set exhibits the effects of additional source, i.e., anisotropy. The isotropic system is resolved by assuming the metric potentials proposed by Krori-Barua while the second set needs one constraint to be solved. The physical acceptability and consistency of the obtained solutions are analyzed through graphical analysis of effective matter components and energy bounds. We also examine mass, surface redshift and compactness of the resulting solutions. For particular values of the decoupling parameter, our both solutions turn out to be viable and stable. We conclude that this curvature-matter coupling gravity provides more stable solutions corresponding to a self-gravitating geometry.

Highlights

Einstein theory of general relativity (GR) has been considered as the root of cosmology and gravitational phenomena
The virial mass discrepancy at the galactic cluster level and the galaxy rotation curves [1,2], cosmic accelerated expansion as well as other cosmological observations suggest that the standard general relativistic gravitational field equations, based on the Einstein-Hilbert (EH) action cannot describe the universe at large scales
This paper investigates the influence of f (R, T, Q) correction terms on two anisotropic solutions obtained through minimal geometric deformation (MGD) approach for spherical spacetime

Summary

Introduction

Einstein theory of general relativity (GR) has been considered as the root of cosmology and gravitational phenomena. The role of dark matter and dark energy, without resorting to exotic matter distribution is explained through the modification in the EH action Several extended theories such as f (R, Lm) and f (R, T) engage such arbitrary coupling but their functionals cannot be considered in the most general form to understand the effects of coupling on celestial objects in some situations. One cannot explain coupling effects on the gravitational model in f (R, T) theory when trace-free EMT (i.e., T = 0) is considered, while f (R, T, Q) gravity studies such effects even in this context. Sharif and Majid [42,43,44] considered different known isotropic solutions and found anisotropic spherical solutions with the help of minimal and extended version of the decoupling scheme in Brans-Dicke theory.

Gravitational Decoupling

Anisotropic Solutions

Solution I

Solution II

Conclusions