Characterization of gravitational waves from spinning compact binaries

Some characterizations of gravitational waves emitted from the 2.5 post-Newtonian order Lagrangian dynamics of spinning compact binaries including the next-order spin-orbit contribution and the radiative reaction are detailed. The relationship between the regular and chaotic dynamics and the gravitational waveforms is also described. When the radiative reaction term does not appear in the equations of motion, the gravitational waves are periodic/quasi-periodic for an order conservative binary system, but they seem to be typically irregular for a chaotic one. On the other hand, the binary systems become dissipative and should coalesce if the radiative reaction term is added to the equations of motion. In the dissipative case, the original ordered conservative system can still give regular gravitational waveforms in such a long time before the occurrence of the merging orbits. However, the coalescence time of the binary system corresponding to its original chaotic conservative system is too short to obtain enough information about the characterization of the gravitational waveforms.