Using MGD gravitational decoupling to extend the isotropic solutions of Einstein equations to the anisotropical domain

TL;DR

This paper uses the minimal geometric deformation (MGD) method to generate new anisotropic solutions from known isotropic solutions of Einstein's equations, specifically extending the Finch-Skea solution.

Contribution

It introduces a systematic approach to decouple Einstein equations using MGD, enabling the derivation of new anisotropic solutions from existing isotropic ones.

Findings

Derived new anisotropic solutions from Finch-Skea isotropic solution.

Identified parameter intervals for physically viable solutions.

Demonstrated the applicability of MGD in extending isotropic to anisotropic models.

Abstract

The aim of this work is to obtain new analitical solutions for Einstein equations in the anisotropical domain. This will be done via the minimal geometric deformation (MGD) approach, which is a simple and systematical method that allow us to decouple the Einstein equations. It requires a perfect fluid known solution that we will choose to be Finch-Skeas(FS) solution. Two different constraints were applied, and in each case we found an interval of values for the free parameters, where necesarly other physical solutions shall live.