An approximate binary-black-hole metric

TL;DR

This paper develops an approximate spacetime metric for two widely-separated non-rotating black holes in orbit, useful for numerical simulations and initial data in binary black hole studies.

Contribution

It introduces a novel method of matching post-Newtonian and perturbed Schwarzschild metrics into a single coordinate system for binary black holes.

Findings

Provides a metric valid up to black hole horizons

Initial data free of spurious gravitational waves

Applicable to early inspiral phase simulations

Abstract

An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric is presented in a single coordinate system valid up to the apparent horizons of the black holes. This metric could be useful in numerical simulations of binary black holes. Initial data extracted from this metric have the advantages of being linked to the early inspiral phase of the binary system, and of not containing spurious gravitational waves.