The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.

We study the motion of neutral and charged spinning bodies in curved spacetime in the test-particle limit. We construct equations of motion using a closed covariant Poisson-Dirac bracket formulation that allows for different choices of the Hamiltonian. We derive conditions for the existence of constants of motion and apply the formalism to the case of spherically symmetric spacetimes. We show that the periastron of a spinning body in a stable orbit in a Schwarzschild or Reissner-Nordstrøm background not only precesses but also varies radially. By analyzing the stability conditions for circular motion we find the innermost stable circular orbit (ISCO) as a function of spin. It turns out that there is an absolute lower limit on the ISCOs for increasing prograde spin. Finally we establish that the equations of motion can also be derived from the Einstein equations using an appropriate energy-momentum tensor for spinning particles.

Among the sources of gravitational waves worth modelling there are Extreme Mass Ratio binaries. In order to understand the dynamics during their coalescence, we describe a special class of ballistic geodesics in Schwarzschild space-time. These orbits are in 1-1 correspondence with stable circular orbits. From these special orbits we derive analytic expressions for the source terms in the Regge-Wheeler radiative equations for a point-particle, and compute the gravitational waves emitted during the infall in an Extreme Mass Ratio black-hole binary coalescence. Results of these calculations and the wave-forms obtained are then discussed, showing limits and applicability of the method, among which the recognition of a universal geodetic behaviour in the last phase of plunge.

Among the sources of gravitational waves worth modelling there are Extreme Mass Ratio binaries. In order to understand the dynamics during their coalescence, we describe a special class of ballistic geodesics in Schwarzschild space-time. These orbits are in 1-1 correspondence with stable circular orbits. From these special orbits we derive analytic expressions for the source terms in the Regge-Wheeler radiative equations for a pointparticle, and compute the gravitational waves emitted during the infall in an Extreme Mass Ratio black-hole binary coalescence. Results of these calculations and the waveforms obtained are then discussed, showing limits and applicability of the method, among which the recognition of a universal geodetic behaviour in the last phase of plunge.