# A general interior anisotropic solution for a BTZ vacuum in the context of the Minimal Geometric Deformation decoupling approach

## TL;DR

This paper develops a method to generate general static interior solutions for a BTZ vacuum in 2+1 dimensions using the Minimal Geometric Deformation approach, with the energy density as a key generating function.

## Contribution

It introduces a novel application of the MGD decoupling method to derive interior solutions for BTZ vacuum spacetimes, emphasizing the role of energy density as a generator.

## Key findings

- Solution generated solely by the energy density of the isotropic sector
- Method applicable to various energy density profiles
- Potential to model complex stellar structures in 2+1 dimensions

## Abstract

In this work we implement the Minimal Geometric Deformation decoupling method to obtain general static interior solutions for a BTZ vacuum from the most general isotropic solution in $2+1$ dimensions including the cosmological constant $\Lambda$. We obtain that the general solution can be generated only by the energy density of the original isotropic sector, so that this quantity plays the role of a generating function. Although as a particular example we study the static star with constant density, the method here developed can be easily applied to more complex situations described by other energy density profiles.