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Orbital eccentricity in general relativity from catastrophe theory

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arxiv 2411.00098 v2 pith:PN4TY44O submitted 2024-10-31 gr-qc astro-ph.HE

Matteo Boschini , Nicholas Loutrel , Davide Gerosa , Giulia Fumagalli This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords eccentricityrelativityorbitalgeneralcatastropheestimatorfullynumerical
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While the orbital eccentricity is a key feature of the gravitational two-body problem, providing an unambiguous definition in general relativity poses significant challenges. Despite such foundational issue, the eccentricity of binary black holes has important implications in gravitational-wave astronomy. We present a novel approach to consistently define the orbital eccentricity in general relativity, grounded in the mathematical field of catastrophe theory. Specifically, we identify the presence of catastrophes, i.e., breakdowns of the stationary-phase approximation, in numerical relativity waveforms and exploit them to develop a robust and fully gauge-invariant estimator of the eccentricity. Our procedure does not require orbital fitting and naturally satisfies the Newtonian limit. The proposed eccentricity estimator agrees with and generalizes a previous proposal, though with a fully independent derivation. We extract gauge-free eccentricity estimates from about 100 numerical relativity simulations and find that the resulting values are systematically lower compared to those reported alongside the simulations themselves.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM

    gr-qc 2024-12 conditional novelty 7.0 of 10

    SEOBNRv5EHM, a new effective-one-body waveform model with third-post-Newtonian eccentricity corrections, reaches a median 0.02% mismatch against eccentric numerical-relativity simulations, about an order of magnitude ...

  2. A geometric template bank for the detection of spinning low-mass compact binaries with moderate orbital eccentricity

    gr-qc 2024-12 conditional novelty 7.0 of 10

    A geometric template bank including eccentricity recovers moderately eccentric BNS/NSBH signals with less than 6% loss, while quasi-circular banks miss up to 40%.

  3. Chase Orbits, not Time: A Scalable Paradigm for Long-Duration Eccentric Gravitational-Wave Surrogates

    gr-qc 2025-09 conditional novelty 6.0 of 10

    Eccentric inspiral waveforms are modeled against mean anomaly rather than time, yielding an order-of-magnitude compression and a 2.77e6 M surrogate that is ~20x faster to evaluate.

  4. Emission and detection of ultra high frequency gravitational waves from highly eccentric orbits of compact binary systems

    gr-qc 2024-12 conditional novelty 6.0 of 10

    For resonant-cavity ultrahigh-frequency gravitational wave searches, eccentric binary orbits deposit more energy in the detector band yet produce lower signal-to-noise ratios than circular orbits, so detection reach i...

  5. Post-Newtonian theory-inspired framework for characterizing eccentricity in gravitational waveforms

    gr-qc 2025-02 conditional novelty 5.0 of 10

    A PN-anchored waveform-based eccentricity estimator using envelope fits to the universal eccentric modulation, with an empirically added half-PN term.

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