Anisotropic solutions by gravitational decoupling

TL;DR

This paper explores a method to generate new anisotropic solutions for static self-gravitating systems by extending isotropic solutions using gravitational decoupling, with detailed matching conditions at the star surface.

Contribution

It introduces a systematic approach to derive physically acceptable anisotropic solutions from known isotropic solutions via gravitational decoupling and minimal geometric deformation.

Findings

New families of anisotropic solutions are generated from isotropic ones.

Matching conditions at the star surface are thoroughly analyzed.

The physical acceptability of solutions is inherited from isotropic parents.

Abstract

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the star surface with the outer Schwarzschild space-time are studied in great details, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.