Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

TL;DR

This paper compares an analytical two-soliton solution with numerical models of rotating neutron stars by matching multipole moments and evaluating key spacetime properties, aiming to validate analytical approximations.

Contribution

It introduces a method to match analytical and numerical solutions of rotating neutron stars using multipole moments and compares various spacetime metrics for validation.

Findings

Good agreement in metric components

Accurate prediction of $R_{ISCO}$ and rotation frequency

Effective matching of multipole moments

Abstract

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit ($R_{ISCO}$), the rotation frequency $\Omega\equiv\frac{d\phi}{dt}$ and the epicyclic frequencies $\Omega_{\rho},\;\Omega_z$. Finally we present some results of the comparison.