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

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.