Comparison of binary black hole initial data sets

Abstract

We present improvements to construction of binary black hole initial data used in SpEC (the Spectral Einstein Code). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision surfaces to be slightly inside rather than on the apparent horizons, thus avoiding extrapolation into the black holes at the last stage of initial data construction. We find that this improves initial data constraint violations near and inside the apparent horizons by about 3 orders of magnitude. We construct several initial data sets that are intended to be astrophysically equivalent but use different free data, boundary conditions, and initial gauge conditions. These include free data chosen as a superposition of two black holes in time-independent horizon-penetrating harmonic and damped harmonic coordinates. We also implement initial data for which the initial gauge satisfies the harmonic and damped harmonic gauge conditions; this can be done independently of the free data, since this amounts to a choice of the time derivatives of the lapse and shift. We compare these initial data sets by evolving them. We show that the gravitational waveforms extracted during the evolution of these different initial data sets agree very well after excluding initial transients. However, we do find small differences between these waveforms, which we attribute to small differences in initial orbital eccentricity, and in initial BH masses and spins, resulting from the different choices of free data. Among the cases considered, we find that superposed harmonic initial data leads to significantly smaller transients, smaller variation in BH spins and masses during these transients, smaller constraint violations, and more computationally efficient evolutions. Finally, we study the impact of initial data choices on the construction of zero-eccentricity initial data.

Matches PRD version. 17 pages, 10 figures

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• Mini-disk accretion onto spinning black hole binaries: quasi-periodicities and outflows
• Targeted large mass ratio numerical relativity surrogate waveform model for GW190814
• The SXS Collaboration's third catalog of binary black hole simulations
• Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory
• Superposed metric for spinning black hole binaries approaching merger
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• Parameter control for eccentric, precessing binary black hole simulations with SpEC
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• Simulating binary black hole mergers using discontinuous Galerkin methods
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• Extending superposed harmonic initial data to higher spin
• Highly accurate simulations of asymmetric black-hole scattering and cross validation of effective-one-body models
• Approaching the black hole by numerical simulations
• Constructing a boosted, spinning black hole in the damped harmonic gauge
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• Microscopic State of BHs and an Exact One Body Method for Binary Dynamics in General Relativity
• Parameter control for binary black hole initial data
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