Integration of the Lane–Emden equation for relativistic anisotropic polytropes through gravitational decoupling: a novel approach

In this work we propose a novel approach to integrate the Lane-Emden equations for relativistic anisotropic polytropes. We take advantage of fact that Gravitational Decoupling allows decrease number degrees freedom once well known solution Einstein field is provided as seed so after demanding polytropic equation radial pressure system automatically closed. The not only extend both isotropic or solutions but simplifies computation Tolman mass whenever Minimal Geometric Deformation considered given $g_{tt}$ component metric remains unchanged. illustrate how method works by analyzing obtained from IV, Durgapal IV and Wymann IIa systems integration.