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

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2022-08, Vol.82 (8), p.1-13, Article 703
• Main Authors: Santana, D., Fuenmayor, E., Contreras, E.
• Format: Article
• Language: English
• Subjects: Anisotropy; Astronomy; Astrophysics and Cosmology; Decoupling; Einstein equations; Elementary Particles; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Neutron stars; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Relativistic effects; String Theory
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-022-10683-5

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