Macroscopic approaches to rotating neutron stars

The macroscopic model for a neutron star (NS) as a perfect liquid drop at equilibrium is extended to rotating systems with a small frequency $\omega $ within the effective-surface (ES) approach. The gradient surface terms of the NS energy density $\cal{E}(\rho)$ in the Equation of State are taken into account along with the volume components at the leading order over the leptodermic parameter $a/R << 1$, where $a$ is the ES crust thickness and $R$ is the mean NS radius. The macroscopic NS angular momentum at small frequencies $\omega$ is used for calculations of the adiabatic moment of inertia (MI) within the Kerr metric approach in the outer Boyer-Lindquist and inner Hogan coordinate forms. The NS MI, $\Theta=\tilde{\Theta}/(1-\cal{G}_{t\varphi})$, was obtained in terms of the statistically averaged MI, $\tilde{\Theta}$, and its time and azimuthal-angle correlation, $\cal{G}_{t\varphi}$, as the sums of volume and surface components. The MI $\Theta$ depends dramatically on the effective radius $R$ due to strong gravitation and surface effects. We found significant additional rotational constraints on the radius $R$ due to the correlation term $\cal{G}_{t\varphi}$ and surface contributions. With these contributions, the adiabaticity condition is better fulfilled for a stronger gravitation in many well-known neutron stars.