Calculating the self force in Schwarzschild spacetime by mode-sum regularization

We outline a method for calculating the self force (the "radiation reaction force") acting on a scalar particle in a strong field orbit in a Schwarzschild spacetime. In this method, the contribution to the self force associated with each multipole mode of the particle's field is calculated separately, and the sum over modes is then evaluated, subject to a certain regularization procedure. We present some explicit results concerning the implementation of the calculation scheme for a static particle, and also for a uniform circular motion, on the Schwarzschild background.