A new family of analytical anisotropic solutions by gravitational decoupling

TL;DR

This paper develops new analytic anisotropic solutions to Einstein's field equations using gravitational decoupling via the Minimal Geometric Deformation method, expanding the set of physically acceptable models for spherically symmetric static objects.

Contribution

It introduces two novel anisotropic solutions derived from Heintzmann's solution applying the MGD method, ensuring physical acceptability of all parameters.

Findings

All parameters meet physical acceptability criteria.

Solutions exhibit well-behaved density and pressure profiles.

Radial and tangential sound speeds are within physical limits.

Abstract

This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric Deformation (MGD). For this we apply MGD to Heintzmann's solution obtaining two new analytic and well behaved anisotropic solutions, in which all their parameters such as the effective density, the effective radial and tangential pressure, as well as radial and tangential sound speed, fulfill each of the requirements for the physical acceptability available in the literature.