Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity

TL;DR

This paper introduces a multi-domain spectral method for generating initial data of arbitrary binary systems in General Relativity, capable of handling black holes, neutron stars, and mixed binaries with high accuracy and efficiency.

Contribution

The method utilizes adapted conformal coordinates and multi-domain spectral expansions to construct initial data for various binary configurations, including black holes and neutron stars, with high precision.

Findings

Successfully constructed initial data for binary black holes and neutron stars.

Achieved high accuracy with moderate computational effort.

Applicable to extreme cases like large mass ratios.

Abstract

We present a multi-domain spectral method to compute initial data of binary systems in General Relativity. By utilizing adapted conformal coordinates, the vacuum region exterior to the gravitational sources is divided up into two subdomains within which the spectral expansion of the field quantities is carried out. If a component of the binary is a neutron star, a further subdomain covering the star's interior is added. As such, the method can be used to construct arbitrary initial data corresponding to binary black holes, binary neutron stars or mixed binaries. In particular, it is possible to describe a black hole component by the puncture ansatz as well as through an excision technique. First examples are given for binary black hole excision data that fulfill the requirements of the quasi-stationary framework, which combines the Conformal Thin Sandwich formulation of the constraint equations with the Isolated Horizon conditions for black holes in quasi-equilibrium. These numerical solutions were obtained to extremely high accuracy with moderate computational effort. Moreover, the method proves to be applicable even when tending toward limiting cases such as large mass ratios of the binary components.