Non-rotating and slowly rotating stars in classical physics

Abstract

Equations are given for the calculation of the equilibrium configurations of slowly rotating stars in the framework of classical physics. In particular, prescriptions have been given to find the mass-radius, the mass-central density relations and the shapes of rotating stars. The equations which determine the relations between mass, central density and radius of rotating configurations take the form of an equation of hydrostatic equilibrium. These equations show the balance between the pressure, gravitational, and centrifugal forces correctly to second order in the angular velocity, but no other approximation is made. The equations which determine the moment of inertia and the quadru-pole moment of the rotating star have also been derived.