Building post-Newtonian neutron stars

TL;DR

This paper explores the accuracy of modeling neutron stars with the post-Newtonian approximation, highlighting formulation flexibility and introducing a new simplified method for constructing neutron star models.

Contribution

It analyzes the degrees of freedom in post-Newtonian formulations and proposes a novel scaling-based strategy for building neutron star models in isotropic coordinates.

Findings

Significant flexibility in post-Newtonian stellar structure equations

Demonstrated impact of formulation choices on neutron star models

Introduced a new scaling method simplifying neutron star construction

Abstract

Owed to their compactness, neutron stars involve strong gravity and extreme density physics. Nevertheless, at present, there are a variety of problems where progress (at least conceptually) can be made in the context of weak gravity. Motivated by this we examine how accurately one can model neutron stars using the post-Newtonian approximation to general relativity. In general, we find there is a significant degree of freedom in how the post-Newtonian equations of stellar structure can be formulated. We discuss this flexibility in the formulation and provide examples to demonstrate the impact on stellar models. We also consider the (closely related) problem of building neutron stars using isotropic coordinates. In this context, we provide a new strategy for solving the equations (based on a scaling argument) which significantly simplifies the problem.