Numerical method for binary black hole/neutron star initial data: Code test

TL;DR

This paper introduces a new numerical method using multiple spherical coordinate patches to generate initial data for binary black hole/neutron star systems, with detailed convergence tests and application examples.

Contribution

The paper presents a novel multi-patch numerical approach for constructing initial data in binary compact object simulations, improving accuracy and convergence.

Findings

Successful calibration with analytic solutions

Effective treatment of boundary conditions

Initial data for binary black holes demonstrated

Abstract

A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green's function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green's functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.