Efficient Eccentric Effective-One-Body Dynamics via Near-Identity Averaging Transformations
Abstract
Next-generation gravitational-wave detectors, such as LISA, the Einstein Telescope, and Cosmic Explorer, will require accurate and efficient models of long-lived black hole binary signals, including those with significant eccentricity. A challenge for eccentric effective-one-body models is the cost of resolving rapidly oscillating orbital dynamics over the inspiral, particularly for low-mass and large-mass-ratio systems. We address this by recasting the nonspinning eccentric effective-one-body equations of motion in terms of osculating orbital elements and then applying near-identity averaging transformations to eliminate the fast orbital-timescale structure during the inspiral. Each order in this procedure suppresses the oscillatory behavior by one factor of the ratio of orbital to radiation-reaction timescales. The resulting averaged dynamics are evolved on the radiation-reaction timescale, and then the system is mapped back to the full EOB dynamics for the final transition to plunge. This reduces the cost of the inspiral dynamics by up to two orders of magnitude, eliminating this as the primary bottleneck for long waveforms. The overall waveform-generation speedup spans 1.5 − 8 ×, motivating the development of more efficient waveform-generation methods. We also validate the accuracy of the method by comparing waveforms generated from the averaged and full effective-one-body dynamics across a broad region of parameter space for moderate to large eccentricities. Carrying out this averaging procedure to next-to-next-to-leading order is needed to accurately model comparable-mass binaries, yielding mismatches ≤ 8.05 × 10−5. These results establish near-identity averaging as a practical route to efficient eccentric effective-one-body inspirals, and provide a foundation for further extensions to low-eccentricity and spinning waveform models.
Versions
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BibTeX
@misc{lynch2026efficient,
title = {{Efficient Eccentric Effective-One-Body Dynamics via Near-Identity Averaging Transformations}},
author = {Philip Lynch and Alessandra Buonanno and Aldo Gamboa and Maarten van de Meent},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.30594},
eprint = {2606.30594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30594},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient Eccentric Effective-One-Body Dynamics via Near-Identity Averaging Transformations
AU - Philip Lynch
AU - Alessandra Buonanno
AU - Aldo Gamboa
AU - Maarten van de Meent
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2606.30594
UR - https://arxiv.org/abs/2606.30594
AB - Next-generation gravitational-wave detectors, such as LISA, the Einstein Telescope, and Cosmic Explorer, will require accurate and efficient models of long-lived black hole binary signals, including those with significant eccentricity. A challenge for eccentric effective-one-body models is the cost of resolving rapidly oscillating orbital dynamics over the inspiral, particularly for low-mass and large-mass-ratio systems. We address this by recasting the nonspinning eccentric effective-one-body equations of motion in terms of osculating orbital elements and then applying near-identity averaging transformations to eliminate the fast orbital-timescale structure during the inspiral. Each order in this procedure suppresses the oscillatory behavior by one factor of the ratio of orbital to radiation-reaction timescales. The resulting averaged dynamics are evolved on the radiation-reaction timescale, and then the system is mapped back to the full EOB dynamics for the final transition to plunge. This reduces the cost of the inspiral dynamics by up to two orders of magnitude, eliminating this as the primary bottleneck for long waveforms. The overall waveform-generation speedup spans 1.5 − 8 ×, motivating the development of more efficient waveform-generation methods. We also validate the accuracy of the method by comparing waveforms generated from the averaged and full effective-one-body dynamics across a broad region of parameter space for moderate to large eccentricities. Carrying out this averaging procedure to next-to-next-to-leading order is needed to accurately model comparable-mass binaries, yielding mismatches ≤ 8.05 × 10^−5. These results establish near-identity averaging as a practical route to efficient eccentric effective-one-body inspirals, and provide a foundation for further extensions to low-eccentricity and spinning waveform models.
ER -