Truncated post-Newtonian neutron star model

TL;DR

This paper develops a truncated post-Newtonian model for neutron stars by expanding the hydrostatic equilibrium equations and solving the resulting system, providing a useful approximation for future binary neutron star simulations.

Contribution

It introduces a truncated post-Newtonian approach to model neutron stars, demonstrating convergence and accuracy compared to full general relativity.

Findings

Second post-Newtonian approximation closely matches general relativistic results.

The method shows convergence in mass-radius relations with increasing order.

The approach provides a practical tool for binary neutron star studies.

Abstract

As a preliminary step towards simulating binary neutron star coalescing problem, we test a post-Newtonian approach by constructing a single neutron star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic equilibrium by the power of $c^{-2}$, where $c$ is the speed of light, and truncate at the various order. We solve the system using the polytropic equation of state with index $\Gamma=5/3, 2$ and 3, and show how this approximation converges together with mass-radius relations. Next, we solve the Hamiltonian constraint equation with these density profiles as trial functions, and examine the differences in the final metric. We conclude the second `post-Newtonian' approximation is close enough to describe general relativistic single star. The result of this report will be useful for further binary studies. (Note to readers) This paper was accepted for publication in Physical Review D. [access code dsj637]. However, since I was strongly suggested that the contents of this paper should be included as a section in our group's future paper, I gave up the publication.