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The study of unbound binary–black-hole encounters provides a gauge-invariant approach to exploring strong-field gravitational interactions in two-body systems, which can subsequently inform waveform models for bound orbits. In this work, we present 60 new highly accurate numerical relativity (NR) simulations of black-hole scattering, generated using the Spectral Einstein Code. Our simulations include 14 spin-aligned configurations, as well as 16 configurations with unequal masses, up to a mass ratio of 10. We perform the first direct comparison of scattering angles computed using different NR codes, finding good agreement. We compare our NR scattering angle results to the post-Minkowskian-based effective-one-body (EOB) closed-form models and , finding less than 5% deviation except near the scatter-capture separatrix. Comparisons with the post-Newtonian-based EOB evolution models and reveal that the former agrees within 8% accuracy with nonspinning NR results across most parameter ranges, whereas the latter matches similarly at lower energies but diverges significantly at higher energies. Both evolution EOB models exhibit increased deviations for spinning systems, predicting a notably different location of the capture separatrix compared to NR. Our key result is the first measurement of disparate scattering angles from NR simulations due to asymmetric gravitational-wave emission. We compare these results to models constructed to calculate the scattering angle of a single black hole in asymmetric systems.
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This content will become publicly available on December 1, 2026
Black-hole scattering with numerical relativity: Self-force extraction and post-Minkowskian validation
The asymptotic nature of unbound binary-black-hole encounters provides a clean method for comparing different approaches for modeling the two-body problem in general relativity. In this work, we use numerical relativity simulations of black-hole scattering, generated using the Spectral Einstein Code, to explore the self-force and post-Minkowskian expansions of the scattering angle. First, we use a set of unequal-mass simulations to extract the self-force contributions to the scattering angle. Our main result is that using information up to second-order in the symmetric mass ratio (2SF) reproduces numerical relativity within the error bars across the full range of mass-ratios, including equal mass. Next, we compare our numerical relativity results to state-of-the-art post-Minkowskian predictions at larger impact parameters than previously explored. We find good agreement in the weak-field regime and discuss the relative importance of higher order terms.
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- Award ID(s):
- 2308615
- PAR ID:
- 10697294
- Publisher / Repository:
- APS
- Date Published:
- Journal Name:
- Physical Review D
- Volume:
- 112
- Issue:
- 12
- ISSN:
- 2470-0010
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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