This paper introduces SEOBNRv6EPHM, a new model for the gravitational waves emitted when two black holes orbit and merge. The model can follow systems whose orbits are not perfect circles (eccentricity) and whose spins are tilted so the orbital plane wobbles (spin precession). Both of these effects leave clear fingerprints on the gravitational-wave signal and are important for understanding how the binary formed.

The authors build SEOBNRv6EPHM within the effective-one-body (EOB) framework. In plain terms, EOB turns the two-body problem into an easier problem of a single body moving in an effective spacetime. The model produces the full signal from the long inspiral through the final merger and ringdown. It also handles dynamical captures and scattering encounters, not just simple bound orbits. To get realistic results the team combines analytical formulas from post-Newtonian theory (a controlled expansion for weak gravity), resums them into more stable forms, and tunes some parameters to accurate but costly numerical relativity simulations. The waveforms are generated in a rotating frame that follows the orbital plane and then “twisted up” back into the observer frame, a standard trick to include precession.

The paper reports the first systematic test of a generic-orbit, spin-precessing model against many numerical-relativity waveforms. The authors compared their model to 1,437 quasi-circular simulations and 87 eccentric simulations. Median waveform mismatches — a measure of difference between two waveforms where lower is better — remain below about 1 percent. That matches the accuracy of the best quasi-circular SEOBNR model (SEOBNRv5PHM) and improves on the previous generic-orbit model TEOBResumS-Dalí by roughly a factor of four in median mismatch. The new model also reproduces non-perturbative behavior seen in numerical studies of scattering black holes.