Comparing initial-data sets for binary black holes

TL;DR

This paper compares different methods for constructing initial data for binary black hole simulations, revealing significant differences and potential unphysical gravitational radiation in current approaches, emphasizing the need for more realistic initial data.

Contribution

It systematically compares three decompositions of Einstein's constraint equations for binary black hole initial data, highlighting the impact of freely specifiable data choices.

Findings

Initial data sets differ significantly, with up to 5% variation in ADM energy.

Current initial data may contain unphysical gravitational radiation of several percent of total mass.

Choice of extrinsic curvature influences data more than conformal metric.

Abstract

We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two Kerr-Schild black holes to fix the freely specifiable data. We find that these initial-data sets differ significantly, with the ADM energy varying by as much as 5% of the total mass. We find that all initial-data sets currently used for evolutions might contain unphysical gravitational radiation of the order of several percent of the total mass. This is comparable to the amount of gravitational-wave energy observed during the evolved collision. More astrophysically realistic initial data will require more careful choices of the freely specifiable data and boundary conditions for both the metric and extrinsic curvature. However, we find that the choice of extrinsic curvature affects the resulting data sets more strongly than the choice of conformal metric.