Relativistic anisotropic stars with the polytropic equation of state in general relativity

TL;DR

This paper investigates relativistic, pressure-anisotropic stars with a polytropic equation of state within general relativity, deriving modified equations, finding analytical solutions for incompressible stars, and analyzing their stability.

Contribution

It introduces modified Lane-Emden equations for anisotropic stars and provides analytical solutions and stability analysis within the relativistic framework.

Findings

Derived modified Lane-Emden equations for anisotropic stars

Obtained analytical solutions for incompressible fluid stars

Studied stability against radial oscillations

Abstract

Spherically symmetric relativistic stars with the polytropic equation of state, which possess the local pressure anisotropy, are considered in the context of general relativity. The modified Lane-Emden equations are derived for the special ansatz for the anisotropy parameter $\Delta$ in the form of the differential relation between $\Delta$ and the metric function $\nu$. The analytical solutions of the obtained equations are found for incompressible fluid stars. The dynamical stability of incompressible anisotropic fluid stars against radial oscillations is studied.