Are different approaches to constructing initial data for binary black hole simulations of the same astrophysical situation equivalent?

TL;DR

This paper compares two different initial data schemes for binary black hole simulations, showing they produce nearly identical gravitational waveforms and remnant properties, thus establishing their astrophysical equivalence.

Contribution

The study demonstrates the consistency and equivalence of conformally flat and conformally curved initial data schemes in binary black hole simulations for nonspinning systems.

Findings

Waveform phase difference less than 0.01 radians

Amplitude difference less than 0.5%

Final black hole mass and spin agree within 10^{-5}

Abstract

Initial data for numerical evolutions of binary-black holes have been dominated by "conformally flat" (CF) data (i.e., initial data where the conformal background metric is chosen to be flat) because they are easy to construct. However, CF initial data cannot simulate nearly extremal spins, while more complicated "conformally curved" initial data (i.e., initial data in which the background metric is \emph{not} explicitly chosen to be flat), such as initial data where the spatial metric is chosen to be proportional to a weighted superposition of two Kerr-Schild (SKS) black holes can. Here we establish the consistency between the astrophysical results of these two initial data schemes for nonspinning binary systems. We evolve the inspiral, merger, and ringdown of two equal-mass, nonspinning black holes using SKS initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within $\delta \phi \lesssim 10^{-2}$ radians and the amplitudes agree to within $\delta A/A \lesssim 5 \times 10^{-3}$, which are within the numerical errors of the simulations. Furthermore, we find that the final mass and spin of the remnant black hole agree to one part in $10^{5}