Gravitational self-force effects on a point mass moving around a Schwarzschild black hole

We consider the effects of the gravitational self-force on a point mass moving in a generic (eccentric) orbit around a Schwarzschild black hole. We developed a numerical code to solve the metric perturbation equations in the time domain, under the Lorenz gauge condition, and to implement the so-called 'mode sum' scheme to obtain the self-force. We use our numerical results to investigate both dissipative and conservative self-force effects on the particle's orbits. To check the consistency of our calculation, we (1) compare our results with independent calculations based on a different gauge, in the special case of a circular orbit (by considering gauge-invariant quantities); (2) derive the energy and angular momentum fluxes of emitted gravitational waves and compare with results from standard Teukolsky-based calculations.