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

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.