Relativistic Numerical Method for Close Neutron Star Binaries

TL;DR

This paper introduces a numerical method for simulating the complex dynamics of coalescing neutron star binaries within general relativity, incorporating gravitational radiation effects through a multipole expansion.

Contribution

It presents a novel computational approach that combines conformally flat spacetime with multipole expansion to model neutron star mergers including gravitational wave emission.

Findings

Successfully models neutron star coalescence in 3+1 dimensions

Incorporates gravitational radiation effects via multipole expansion

Allows for the study of gravitational wave signals from mergers

Abstract

We describe a numerical method for calculating the (3+1) dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial 3-metric chosen to be conformally flat. Against this solution to the general relativistic field equations the hydrodynamic variables and gravitational radiation are allowed to respond. The gravitational radiation signal is derived via a multipole expansion of the metric perturbation to the hexadecapole order including both mass and current moments and a correction for the slow motion approximation. Using this expansion, the effect of gravitational radiation on the system evolution can also be recovered by introducing an acceleration term in the matter evolution.