Post-Newtonian evolution of massive black hole triplets in galactic nuclei.

Massive black-hole binaries (MBHBs) are thought to be the main source of gravitational waves (GWs) in the low-frequency domain surveyed by Pulsar Timing Array (PTA) campaigns and space-borne missions (LISA). However, many MBHBs in realistic astrophysical environments may not reach separations small enough to allow significant GW emission. This final-parsec problem can be eased by the appearance of a third massive black hole (MBH) whose action can force, under certain conditions, the former MBHB to merge. A detailed assessment of the process requires a general relativistic treatment and the inclusion of environmental effects. In this thesis, I developed a three-body Post-Newtonian (PN) code framed in a galactic potential, including PN terms up to 2.5PN order, orbital hardening and dynamical friction. With the code I performed a vast exploration of the parameter space represented by MBH triplets. I found that a non-negligible fraction (_ 30%) of the otherwise stalled binaries can actually merge because of the perturbation of the third body. By combining these results with a cosmological semi-analytical code of galaxy formation, I drew robust predictions about the nHz stochastic background of GWs, which in the most pessimistic scenario is suppressed by only a factor of two with respect to the standard models in which MBHBs can efficiently merge. This result has important consequences for PTA and implies that a detection of the GW background could be claimed in the near future.