https://doi.org/10.1140/epjc/s10052-022-10683-5
Regular Article - Theoretical Physics
Integration of the Lane–Emden equation for relativistic anisotropic polytropes through gravitational decoupling: a novel approach
1
Departamento de Física, Colegio de Ciencias e Ingeniería, Universidad San Francisco de Quito, Quito, Ecuador
2
Centro de Física Teórica y Computacional, Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, 1050, Caracas, Venezuela
Received:
29
April
2022
Accepted:
6
August
2022
Published online:
13
August
2022
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 
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.
© The Author(s) 2022
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