Numerical Treatment Of Hartle'S Perturbation Method For Differentially Rotating Neutron Stars Simulated By General-Relativistic Polytropic Models

We compute general-relativistic polytropic models of differentially rotating neutron stars. A brief description of our numerical treatment is given as follows. First, the relativistic Oppenheimer–Volkoff equations of hydrostatic equilibrium are solved for nonrotating models obeying the well-known polytropic equation of state. Then, uniform rotation assumed for such models is treated in the framework of Hartle's perturbation method; thus, corrections to mass and radius, owing to spherical and quadrupole deformations, are calculated. Next, a perturbative approach to the stellar structure up to terms of third order in the angular velocity is carried out; angular momentum,J, moment of inertia,I, rotational kinetic energy,T, and gravitational potential energy,W, are quantities drastically corrected by the third-order approach. Finally, assuming that our polytropic models satisfy a particular differential rotation law, we compute the increase in mass and in some other significant physical characteristics owing to the differential rotation.