Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity

We present a first complete implementation of an effective-one-body (EOB) model for extreme-mass-ratio inspirals (EMRIs) that incorporates aligned spins (on both the primary and the secondary) as well as orbital eccentricity. The model extends TEOBResumS-Dal\'{} for these binaries by (i) recasting conservative first-order gravitational self-force (1GSF) information in the resummed EOB potentials, (ii) employing a post-Newtonian (PN) 3⁺¹⁹PN-accurate (3PN comparable-mass terms hybridized with test-particle terms up to 22PN relative order) expression for the gravitational-wave flux at infinity, and (iii) using an improved implementation of the horizon flux that better approximates its test-mass representation. With respect to our previous work [A. Albertini et al., Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large-mass-ratio case, Phys. Rev. D 106, 084062 (2022).], we demonstrate that the inclusion of the 3⁺¹⁹PN-accurate =9 and =10 modes in the flux at infinity significantly improves the model's agreement with second-order accurate GSF (2GSF) circular waveforms. For a standard EMRI with mass ratio q≡m₁/m₂=5×10⁴ and m₂=10M_, the accumulated EOB/2GSF dephasing is rad for ~1 yr of evolution, which is consistent with the standard accuracy requirements for EMRIs. We also showcase the generation of eccentric and spinning waveforms and discuss future extensions of our EOB towards a physically complete model for EMRIs.