Minimal Geometric Deformation: the inverse problem

TL;DR

This paper introduces a method to derive isotropic solutions from anisotropic solutions of Einstein's equations using Minimal Geometric Deformation, demonstrated through a static wormhole example.

Contribution

It develops a systematic approach to invert anisotropic solutions into isotropic sources within the MGD-decoupling framework.

Findings

Any static, spherically symmetric anisotropic solution can be generated from an isotropic source.

The method successfully applied to a traversable wormhole model.

Provides a new tool for analyzing anisotropic spacetimes in general relativity.

Abstract

In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric Deformation-decoupling approach. To be more precise, we developed a mechanism to obtain an isotropic solution from any anisotropic solution of the Einstein field equations. As an example, we implement the method to obtain the sources of a simple static anisotropic and spherically symmetric traversable wormhole.