Complexity factor of spherically anisotropic polytropes from gravitational decoupling

TL;DR

This paper analyzes the complexity factor of spherically symmetric polytropic matter distributions using gravitational decoupling, deriving analytic solutions and constructing a specific model with Tolman IV as a seed.

Contribution

It introduces a method to compute the complexity factor for polytropic spheres via gravitational decoupling, providing new analytic solutions in general relativity.

Findings

Derived analytic solutions for polytropic spheres

Constructed a specific model using Tolman IV seed solution

Demonstrated the application of gravitational decoupling to complexity analysis

Abstract

In this work we will analyse the complexity factor, proposed by L. Herrera, for spherically symmetric static matter distributions satisfying a polytropic equation through the gravitational decoupling method. Specifically, we will use the 2-step GD, which is a particular case of the extended geometric deformation (EGD), to obtain analytic polytropic solutions of Einstein's equations. In order to give an example, we construct a model satisfying a polytropic equation of state using Tolman IV as a seed solution.