Accuracy and Applicability of the Hartle-Thorne and Komatsu-Eriguchi-Hachisu Methods for Modeling Rotating Neutron Stars

Neutron stars, which are composed of extremely dense nuclear matter, serve as natural laboratories to study nuclear interactions beyond the terrestrial experiments. Recent researches have actively explored how the equation of state (EoS) can be constrained by observed neutron star masses and radii, and how nuclear interactions affect their macroscopic properties. Most of these studies, however, rely on the Tolman-Oppenheimer-Volkoff (TOV) equations, which assumed static, spherically symmetric neutron stars. Since neutron stars are rotating objects and thus axisymmetrically deformed, the TOV calculation may be insufficient to capture their realistic structure. In this work, we investigate the influence of nuclear matter properties on the physical quantities of rotating neutron stars using two approaches: the perturbative Hartle-Thorne (HT) method and fully general relativistic Komatsu-Eriguchi-Hachisu (KEH) method. For nuclear EoS parameter sets, we emamine the OMEG series, in which the slope of the symmetry energy $L$ is systematically varied. We find that rotational effects lead to a noticeable increase in the stellar radius, which depends sensitively on values of $L$. Additionally, focusing on the rotational deformation, we show that the results obtained by these two methods deviate each other even for the slowly rotating case such as $\Omega=200$ Hz. These results reveal that, for detailed discussions on the internal structure and stability of rotating neutron stars, the fully general relativistic method such as KEH is indispensable.