  In a compact binary coalescence, the spins of the compact objects can have a
significant effect on the orbital motion and gravitational-wave (GW) emission.
For generic spin orientations, the orbital plane precesses, leading to
characteristic modulations of the GW signal. The observation of precession
effects is crucial to discriminate among different binary formation scenarios,
and to carry out precise tests of General Relativity. Here, we work toward an
improved description of spin effects in binary inspirals, within the
effective-one-body (EOB) formalism, which is commonly used to build waveform
models for LIGO and Virgo data analysis. We derive EOB Hamiltonians including
the complete fourth post-Newtonian (4PN) conservative dynamics, which is the
current state of the art. We place no restrictions on the spin orientations or
magnitudes, or on the type of compact object (e.g., black hole or neutron
star), and we produce the first generic-spin EOB Hamiltonians complete at 4PN
order. We consider multiple spinning EOB Hamiltonians, which are more or less
direct extensions of the varieties found in previous literature, and we suggest
another simplified variant. Finally, we compare the circular-orbit,
aligned-spin binding-energy functions derived from the EOB Hamiltonians to
numerical-relativity simulations of the late inspiral. While finding that all
proposed Hamiltonians perform reasonably well, we point out some interesting
differences, which could guide the selection of a simpler, and thus
faster-to-evolve EOB Hamiltonian to be used in future LIGO and Virgo inference
studies.
