Minimal geometric deformation decoupling in $2+1$ dimensional space-times

TL;DR

This paper explores minimal geometric deformation decoupling in 2+1 dimensional spacetimes, enabling the derivation of anisotropic solutions from isotropic ones, including new solutions based on the BTZ black hole.

Contribution

It introduces a method for generating anisotropic solutions in 2+1 dimensions using minimal geometric deformation, contrasting with 3+1 dimensional cases.

Findings

Both isotropic and anisotropic sectors satisfy Einstein equations in 2+1 dimensions.

New anisotropic solutions derived from the static BTZ black hole.

Abstract

We study the minimal geometric deformation decoupling in $2+1$ dimensional space--times and implement it as a tool for obtaining anisotropic solutions from isotropic geometries. Interestingly, both the isotropic and the anisotropic sector fulfill Einstein field equations in contrast to the cases studied in $3+1$ dimensions. In particular, new anisotropic solutions are obtained from the well known static BTZ solution.