Gravitational decoupled anisotropies in compact stars

TL;DR

This paper introduces a systematic method to generate and analyze anisotropic models of compact stars by extending isotropic solutions through minimal geometric deformation, facilitating the study of observational effects like redshift.

Contribution

It presents a novel application of the minimal geometric deformation approach to decouple and model anisotropies in compact stars systematically.

Findings

Anisotropic solutions are derived from isotropic models using minimal geometric deformation.

The approach allows for systematic manipulation of anisotropies in stellar models.

The noncommutativity of the method leads to different physically acceptable solutions when applied in reverse order.

Abstract

Simple generic extensions of isotropic Durgapal--Fuloria stars to the anisotropic domain are presented. These anisotropic solutions are obtained by guided minimal deformations over a self gravitating isotropic system. When the isotropic and the anisotropic sector interacts in a purely gravitational manner, the conditions to decouple both sectors by means of the minimal geometric deformation approach are satisfied. Hence the anisotropic field equations are isolated resulting a more treatable set. The simplicity of the equations allows one to manipulate the anisotropies that can be implemented in a systematic way to obtain different realistic models for anisotropic configurations. Later on, observational effects of such anisotropies when measuring the redshift are discussed. To conclude, the application of the method over anisotropic solutions is generalized. In this manner, different anisotropic sectors can be isolated of each other and modeled in a simple and systematic way. Besides, a generic property of the minimal geometric deformation approach, its noncommutativity, is discussed. This property duplicates the solutions obtained through this approach; anisotropies applied in the reversed order give different physically acceptable configurations.