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

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 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 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 superposed Kerr-Schild initial data and compare with an analogous simulation using CF initial data. We find that the resultant gravitational-waveform phases agree to within δϕ≲10^(-2) radians and the amplitudes agree to within δA/A≲5×10^(-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.

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