Fully general relativistic simulation of coalescing binary neutron stars: Preparatory tests

TL;DR

This paper demonstrates the successful development of a 3D general relativistic simulation code capable of stably modeling coalescing binary neutron stars and related test problems, paving the way for realistic long-term astrophysical simulations.

Contribution

The paper introduces a robust numerical framework for fully solving Einstein and hydrodynamic equations in 3D, enabling stable long-term simulations of binary neutron star mergers.

Findings

Simulations of spherical dust collapse and star stability are successful.

The code maintains equilibrium states of rotating neutron stars.

Binary neutron star coalescence can be simulated stably over multiple dynamical timescales.

Abstract

We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation as well as the hydrodynamic equations are fully solved. This paper is especially devoted to simulations of test problems such as spherical dust collapse, stability test of perturbed spherical stars, and preservation of (approximate) equilibrium states of rapidly rotating neutron star and/or corotating binary neutron stars. These test simulations confirm that simulations of coalescing binary neutron stars are feasible in a numerical relativity code. It is illustrated that using our numerical code, simulations of these problems, in particular those of corotating binary neutron stars, can be performed stably and fairly accurately for a couple of dynamical timescales. These numerical results indicate that our formulation for solving the Einstein field equation and hydrodynamic equations are robust and make it possible to perform a realistic simulation of coalescing binary neutron stars for a long time from the innermost circular orbit up to formation of a black hole or neutron star.