Anisotropic ultracompact Schwarzschild star by gravitational decoupling

Abstract

We employ the minimal geometric deformation approach to gravitational decoupling (MGD-decoupling) in order to generate an exact anisotropic and non-uniform version of the ultracompact Schwarzschild star, or 'gravastar', proposed by Mazur and Mottola. This new system represents an ultracompact configuration of radius $R_{S}=2\cal{M}$ whose interior metric can be matched smoothly to a conformally deformed Schwarzschild exterior. Remarkably, the model satisfies some of the basic requirements to describe a stable stellar model, such as a positive density everywhere and decreasing monotonously from the centre, as well as a non-uniform and monotonic pressure.