The general relativistic double polytrope for anisotropic matter

TL;DR

This paper extends a formalism for anisotropic polytropes from Newtonian to relativistic regimes, deriving and solving generalized Lane-Emden equations for models with radial and tangential pressures, and analyzing their physical properties.

Contribution

It introduces a relativistic formalism for anisotropic polytropes with both pressures satisfying a polytropic equation of state, deriving new equations and models.

Findings

Derived generalized Lane-Emden equations for relativistic anisotropic matter

Obtained specific models and analyzed their physical properties

Extended previous Newtonian formalism to relativistic context

Abstract

A general formalism recently proposed to study Newtonian polytropes for anisotropic fluids is here extended to the relativistic regime. Thus, it is assumed that a polytropic equation of state is satisfied by, both, the radial and the tangential pressures of the fluid. Doing so the generalized Lane--Emden equations are obtained and solved. Some specific models are obtained, and their physical properties are discussed.