A new code for equilibriums and quasiequilibrium initial data of compact objects

TL;DR

This paper introduces COCAL, a new computational code for generating equilibrium and quasiequilibrium initial data of compact objects, including black holes, using a flexible multi-patch approach and Green's function methods.

Contribution

The paper presents a novel, simpler code for initial data of compact objects that handles excised regions and multiple patches with second order accuracy.

Findings

Successfully performs convergence tests for black hole data.

Generates binary black hole initial data with equilibrium boundary conditions.

Handles excised regions for black holes within the computational domain.

Abstract

We present a new code, named COCAL - Compact Object CALculator, for the computation of equilibriums and quasiequilibrium initial data sets of single or binary compact objects of all kinds. In the cocal code, those solutions are calculated on one or multiple spherical coordinate patches covering the initial hypersurface up to the asymptotic region. The numerical method used to solve field equations written in elliptic form is an adaptation of self-consistent field iterations in which Green's integral formula is computed using multipole expansions and standard finite difference schemes. We extended the method so that it can be used on a computational domain with excised regions for a black hole and a binary companion. Green's functions are constructed for various types of boundary conditions imposed at the surface of the excised regions for black holes. The numerical methods used in cocal are chosen to make the code simpler than any other recent initial data codes, accepting the second order accuracy for the finite difference schemes. We perform convergence tests for time symmetric single black hole data on a single coordinate patch, and binary black hole data on multiple patches. Then, we apply the code to obtain spatially conformally flat binary black hole initial data using boundary conditions including the one based on the existence of equilibrium apparent horizons.