Evolution dynamics of spinning binaries in effective-one-body theory to fifth Post-Minkowskian order

This paper investigates a self-consistent effective-one-body (EOB) theory developed to describe the dynamics of spinning binary systems. We systematically derive, using field-theoretic principles, all expressions and quantities entering Hamilton’s equations, which govern the dynamical evolution of the system. Based on the effective rotating metric up to fifth post-Minkowskian (PM) order recently obtained by us, we construct the Hamiltonian and the stress-energy tensor. We then derive a decoupled, separable Teukolsky-like equation with a source term for the Newman–Penrose Weyl scalar ${\psi }_4^B$ and present its formal solution. Finally, using this solution, we obtain the energy flux, radiation-reaction force, and gravitational waveforms for the plus'' and cross’’ polarizations generated by spinning binaries. The EOB theory applies to systems with arbitrary mass ratio, which filling the gap between comparable mass ratios and extreme mass ratios.