Characterization of the gravitational wave emission of three black holes

We study the gravitational wave emission of three compact objects using post-Newtonian (PN) equations of motion derived from the Arnowitt-Deser-Misner Hamiltonian formulation, where we include (for the first time in this context) terms up to 2.5 PN order. We perform numerical simulations of a hierarchical configuration of three compact bodies in which a binary system is perturbed by a third, lighter body initially far away from the binary. The relative importance of the different PN orders is examined. We compute the waveform in the linear regime considering mass quadrupole, current quadrupole and mass octupole contributions. Performing a spherical harmonic decomposition of the waveforms we find that from the l = 3 modes it is possible to extract information about the third body, in particular, the period, eccentricity of its orbit, and the inclination angle between the inner and outer binary orbits.