# Decoupling gravitational sources in general relativity: the extended case

## TL;DR

This paper introduces an extended method for decoupling multiple gravitational sources in general relativity, enabling new analyses of black holes, dark matter, and modified gravity effects.

## Contribution

It extends the Minimal Geometric Deformation-decoupling method to a more general form, allowing for the decoupling of complex gravitational systems.

## Key findings

- Successfully decoupled Einstein-Maxwell system to reproduce Reissner-Nordstrom black hole
- Demonstrated potential to analyze modified gravity effects
- Showed applicability to dark matter and hairy black holes

## Abstract

We show how to decoupling two spherically symmetric and static gravitational sources through the most general possible extension of the so-called Minimal Geometric Deformation-decoupling. As a test, we decouple the Einstein-Maxwell system and reproduce the Reissner-Nordstrom black hole solution. We show the potential of this method to study i) the consequences of modified gravity on general relativity, ii) to investigate the conjectured dark matter, and iii) to study hairy black holes.