Self-force and Green function in Schwarzschild spacetime via quasinormal modes and branch cut

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The modelling of gravitational wave sources is of timely interest given the exciting prospect of a first detection of gravitational waves by the new generation of detectors. The motion of a small compact object around a massive black hole deviates from a geodesic due to the action of its own field, giving rise to a self-force and the emission of gravitational waves. The self-force program has recently achieved important results using well-established methods. In this talk, we will present a different, novel method, where the self-force is calculated via the Green function of the wave equation that the field perturbation satisfies. We will present a calculation of the global Green function on Schwarzschild black hole spacetime. The calculation is carried out via a spectroscopy analysis of the Green function, which includes quasinormal modes and a branch cut in the complex-frequency plane. We will apply this analysis to calculate the self-force on a scalar charge and to reveal geometrical properties of wave propagation on a Schwarzschild background.