Class I polytropes for anisotropic matter

A Ramos,E Fuenmayor,C Arias,E Contreras

doi:10.1140/epjc/s10052-021-09002-1

Abstract

In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane–Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both the isothermal and non-isothermal regimes. For completeness, the Tolman mass is computed and analysed to some extend. As a complementary study we consider the impact of the Karmarkar condition on the mass and the Tolman mass functions respectively. Comparison with other results in literature are discussed.

Highlights

Polytropic equations of state have played a remarkable role in astrophysics, and have been extensively used to study the stellar structure
In order to relate the influence of the Karmarkar condition with the mass function m and the Tolman mass, mT, we will take an instructive path to complete our analysis of the fluid distribution of the compact body
We have developed a general method to construct locally anisotropic polytropes, and we have applied it to the specific case of a class I solution for spherically symetric interior space-times

Summary

Introduction

Polytropic equations of state have played a remarkable role in astrophysics (see [1,2] and references therein), and have been extensively used to study the stellar structure. Other approaches as the Randall-Sundrum model [32] or 5-dimensional warped geometries have served as an inspiration for other type of conditions, relating radial derivatives of the metric functions in spherically symmetric spacetimes, that produce self–gravitating spheres embedded in a 5-dimensional flat space-time (embedding class one) In this regard, it is clear that embedding of four-dimensional spacetimes into higher dimensions is a very useful tool in order to generate astrophysical interior models. In this work we consider stellar interiors supported by anisotropic fluids fulfilling the polytropic equation of state for the radial pressure and we implement the class I condition to close the system and construct the corresponding generalized Lane–Emden equation. We will implement the polytropic equation of state to construct the general Lane–Emden equation

Relativistic polytrope for anisotropic fluids

The class I condition

Karmarkar condition and Tolman mass

Conclusions