Analytical approximation of the exterior gravitational field of rotating neutron stars

TL;DR

This paper develops an analytical approximation method for the exterior gravitational field of rotating neutron stars using Bäcklund transformations and Ernst potentials, achieving excellent agreement with numerical models.

Contribution

It introduces a novel approach to approximate the exterior metric of rotating neutron stars analytically using exact solutions and compares it successfully with numerical data.

Findings

Analytic solutions closely match numerical models

Method effectively determines metric from axis data

Few parameters suffice for accurate approximation

Abstract

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.