Uniformly rotating neutron stars

TL;DR

This paper reviews recent advances in modeling uniformly rotating neutron stars using the Hartle formalism, focusing on equilibrium configurations, stability criteria, and mass-radius relations.

Contribution

It extends the Einstein-Maxwell-Thomas-Fermi framework to analyze rotating neutron stars, providing detailed numerical methods and new mass-radius relations.

Findings

Computed static and rotating neutron star properties including mass, radius, and moment of inertia.

Established stability limits based on mass-shedding and secular instability criteria.

Derived maximum mass and minimum rotation period for neutron stars.

Abstract

In this chapter we review the recent results on the equilibrium configurations of static and uniformly rotating neutron stars within the Hartle formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated and extended by Belvedere et al. (2012, 2014). We demonstrate how to conduct numerical integration of these equations for different central densities ${\it \rho}_c$ and angular velocities $\Omega$ and compute the static $M^{stat}$ and rotating $M^{rot}$ masses, polar $R_p$ and equatorial $R_{\rm eq}$ radii, eccentricity $\epsilon$, moment of inertia $I$, angular momentum $J$, as well as the quadrupole moment $Q$ of the rotating configurations. In order to fulfill the stability criteria of rotating neutron stars we take into considerations the Keplerian mass-shedding limit and the axisymmetric secular instability. Furthermore, we construct the novel mass-radius relations, calculate the maximum mass and minimum rotation periods (maximum frequencies) of neutron stars. Eventually, we compare and contrast our results for the globally and locally neutron star models.