Hartle formalism for rotating Newtonian configurations

TL;DR

This paper applies the Hartle formalism to analyze rotating Newtonian stars, deriving key physical properties and demonstrating the method's effectiveness through white dwarf models.

Contribution

It extends the Hartle formalism to Newtonian gravity, providing explicit equations and procedures for calculating properties of rotating stars up to second order in angular velocity.

Findings

Derived equations for rotating stars in Newtonian gravity.

Calculated star properties like mass, radius, and moment of inertia.

Validated the formalism with white dwarf models.

Abstract

We apply the Hartle formalism to study equilibrium configurations in the framework of Newtonian gravity. This approach allows one to study in a simple manner the properties of the interior gravitational field in the case of static as well as stationary rotating stars in hydrostatic equilibrium. It is shown that the gravitational equilibrium conditions reduce to a system of ordinary differential equations which can be integrated numerically. We derive all the relevant equations up to the second order in the angular velocity. Moreover, we find explicitly the total mass, the moment of inertia, the quadrupole moment, the polar and equatorial radii, and the eccentricity of the rotating body. We also present the procedure to calculate the gravitational Love number. We test the formalism in the case of white dwarfs and show its compatibility with the known results in the literature.