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 $\mathcal{E}(\mathcal{\rho })$ [Equation of State] are taken into account along with the volume ones at the leading order of the leptodermic parameter $a\mathrm{/}R<<1$, where $a$ is the ES crust thickness and $R$ is the mean NS radius. The macroscopic NS angular momentum at small frequencies $\omega$ is specified for calculations of the adiabatic moment of inertia (MI) within the Kerr metric coordinate approach in the outer Boyer-Lindquist and inner Hogan forms. The NS MI, $\mathrm{\Theta }=\tilde{\mathrm{\Theta }}\mathrm{/}(1-{\mathcal{G}}_{\mathcal{t}\mathcal{\phi }})$, was obtained in terms of the statistically averaged MI, $\tilde{\mathrm{\Theta }}$, and its time and azimuthal-angle correlation, ${\mathcal{G}}_{\mathcal{t}\mathcal{\phi }}$, as sums of the volume and surface components. The MI $\mathrm{\Theta }$ depends dramatically on its effective radius $R$ because of strong gravitation and surface effects. We found the significant shift of the Schwarzschild radius due to the correlation term ${\mathcal{G}}_{\mathcal{t}\mathcal{\phi }}$. With this term, the adiabaticity condition fails for the NS J0740+6620, with the mass about $M_{\odot }$ for a strong gravitation, in contrast to the NS J0030+0451 for smaller mass, and many other NSs.