MG11 
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Higher-order effects in the dynamics of compact binaries

We investigate the dynamics of spinning compact binaries, including the spin-orbit coupling one post-Newtonian (PN) order beyond its leading contribution, i.e. at the 2.5PN order for black holes with maximal spins. As a first stage, we compute the equations of motion together with the precession equations at the required approximation and derive the first integrals of motion. The spin-spin terms, already known, are systematically ignored. As a second stage, we calculate the spin-orbit part of all multipole moments entering the gravitational-wave energy flux at the relative 2.5PN order. Using a standard energy-balance argument, we finally obtain the 2.5PN spin-orbit effects in the secular evolution of the binary's orbital phase. This results in a very accurate gravitational-wave template to be used in the data analysis of rapidly rotating black-hole binaries in LIGO/Virgo or LISA detectors.