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arXiv · 2510.00531

Consistency of spin effects between numerical relativity and perturbation theory for inspiraling comparable-mass black hole binaries

Tousif Islam·Gaurav Khanna·Scott E. Field
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Abstract

Numerical relativity (NR) provides the most accurate waveforms for comparable-mass binary black holes but becomes prohibitively expensive for increasingly asymmetric mass ratios. Point-particle black hole perturbation theory (ppBHPT), which expands the Einstein equations in the small-mass-ratio limit, offers a computationally efficient alternative but is expected to break down in the comparable-mass regime because it neglects nonlinear effects. Nonetheless, several recent studies have shown that ppBHPT can model non-spinning binaries with high accuracy when supplemented by simple calibrations or a first post-adiabatic (PA) correction. Here we assess the applicability of ppBHPT to quasi-circular binaries with a spinning primary by comparing waveform amplitudes, orbital frequencies, and orbital phases. We find that spin effects in ppBHPT waveforms (without additional spin information beyond adiabatic order) are in surprisingly close agreement with the corresponding NR calculation (outperforming some post-Newtonian models) over the last $\approx 20$ orbital cycles. This suggests that, after incorporating higher-order corrections into ppBHPT waveforms in the non-spinning limit -- via second-order self-force results or semi-analytical fits -- only modest spin-dependent adjustments may be required to achieve NR-faithful ppBHPT waveforms. We also show that combining non-spinning NR information with adiabatic ppBHPT can provide a reasonably accurate inspiral waveform for spins $\chi \lesssim 0.5$ mass ratios $q \gtrsim 5$.

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Tousif Islam, Gaurav Khanna, Scott E. Field. 2025-10-01. Consistency of spin effects between numerical relativity and perturbation theory for inspiraling comparable-mass black hole binaries. https://doi.org/10.1103/9mtw-df24

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