Compact objects by gravitational decoupling in f(R) gravity

M. Sharif,Mariyah Aslam

doi:10.1140/epjc/s10052-021-09436-7

M. Sharif, Mariyah Aslam

Open Access

https://doi.org/10.1140/epjc/s10052-021-09436-7

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Abstract

The objective of this paper is to discuss anisotropic solutions representing static spherical self-gravitating systems in f(R) theory. We employ the extended gravitational decoupling approach and transform temporal as well as radial metric potentials which decomposes the system of non-linear field equations into two arrays: one set corresponding to seed source and the other one involves additional source terms. The domain of the isotropic solution is extended in the background of f(R) Starobinsky model by employing the metric potentials of Krori–Barua spacetime. We determine two anisotropic solutions by employing some physical constraints on the extra source. The values of unknown constants are computed by matching the interior and exterior spacetimes. We inspect the physical viability, equilibrium and stability of the obtained solutions corresponding to the star Her X-I. It is observed that one of the two extensions satisfies all the necessary physical requirements for particular values of the decoupling parameter.

Highlights

It has been observed that the presence of interacting nuclear matter in dense celestial objects leads to the generation of anisotropy [2]
In 1974, the effects of anisotropy on relativistic spherical objects were studied by using specific equations of state (EoS) and an increase in redshift was noted in static models with particular forms of anisotropy [4]
In 2019, Ovalle [26] introduced a novel extension of the minimal geometric deformation (MGD) approach known as extended geometric deformation (EGD)

Summary

Introduction

It has been observed that the presence of interacting nuclear matter in dense celestial objects leads to the generation of anisotropy [2]. Since there is no transfer of energy between matter sources, the interaction between them is purely gravitational To resolve these issues, Casadio et al [25] proposed an extension of the MGD technique by implementing radial as well as temporal transformations and constructed a solution for a static spherical object. In 2019, Ovalle [26] introduced a novel extension of the MGD approach known as extended geometric deformation (EGD) He successfully decoupled two static spherically symmetric gravitational sources and examined its efficiency by recreating the Reissner–Nordström solution. Ξ η represents the additional source which is coupled to gravity through a free parameter χ This source term comprises of new fields which induce anisotropy in self-gravitating bodies. In order to compute these unknowns, we follow a systematic scheme proposed by Ovalle [26]

The extended geometric deformation approach

Junction conditions

Anisotropic interior solutions

Solution I

Solution II

Conclusions