The exterior field of slowly and rapidly rotating neutron stars: Rehabilitating spacetime metrics involving hyperextreme objects

TL;DR

This paper introduces a new exact spacetime metric for neutron stars that accounts for both slow and rapid rotation, comparing its multipole structure with numerical models to highlight the importance of hyperextreme sectors.

Contribution

The paper presents a concise, explicit 4-parameter solution for neutron star exteriors, including hyperextreme objects, and compares its multipole structure with realistic models.

Findings

Hyperextreme sectors are crucial for modeling rapidly rotating neutron stars.

The solution simplifies metric functions for practical applications.

An exact analog of the Hartle-Thorne metric is derived.

Abstract

The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that the hyperextreme sectors of the solution are not less (but possibly even more) important for the correct description of rapidly rotating neutron stars than the subextreme sector involving exclusively the black-hole constituents. We have also worked out in explicit form an exact analog of the well-known Hartle-Thorne approximate metric.