Enabling gravitational-wave astronomy with spin-precessing black holes on generic orbits

Abstract: Binary black holes (BBHs) formed in dense stellar environments or in hierarchical triples can coalesce on eccentric orbits and carry spins of arbitrary orientation, leaving distinctive imprints on their gravitational-wave (GW) emission. We present SEOBNRv6EPHM: the first generic-orbit, spin-precessing model in the effective-one-body SEOBNR family, whose waveforms have underpinned LIGO-Virgo GW analyses since 2011. The model describes the dynamics and multipolar GW signal of generic BBHs, covering the inspiral-merger-ringdown of coalescing binaries and extending to dynamical captures and scattering encounters. We perform the first systematic accuracy assessment of a generic-orbit model against numerical relativity (NR) waveforms of spin-precessing BBHs, using 1437 quasi-circular (QC) and 87 eccentric simulations: median waveform mismatches remain below $1 \%$, matching the accuracy of the QC model SEOBNRv5PHM, and improving on the state-of-the-art generic-orbit model TEOBResumS-Dalí by a median factor of $ 4 $. The model also reproduces the non-perturbative phenomenology observed in NR simulations of generic-spin BBH scattering. It is $\sim 2 - 3$ times faster than SEOBNRv5PHM in the QC limit, and up to an order of magnitude faster than TEOBResumS-Dalí, bringing eccentric inference to the cost of current QC analyses. As a proof of principle, we analyze eleven GW events and focus on GW200129, strengthening its evidence for eccentricity $-$ a result supported by injection-recovery studies with synthetic NR signals of eccentric, spin-precessing BBHs. SEOBNRv6EPHM thus enables, for the first time, accurate and efficient GW analyses that jointly account for eccentricity and spin precession.