Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme

TL;DR

This paper presents a numerical scheme using generalized harmonic coordinates for simulating binary black hole spacetimes, demonstrating effective constraint damping and exploring black hole mergers via scalar field collapse.

Contribution

It introduces detailed methods for harmonic evolution schemes in binary black hole simulations, including constraint damping and source function control, with initial results on black hole coalescence.

Findings

Constraint damping effectively stabilizes simulations

Black hole mergers show zoom-whirl-like behavior

Scalar fields facilitate black hole interaction studies

Abstract

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem. This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation. In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown. Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.