Calculating the Gravitational Self-Force in Schwarzschild Spacetime

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Abstract
We present a practical method for calculating the local gravitational self-force (often called “radiation-reaction force”) for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of mode-sum regularization, in which one first calculates the (finite) contribution to the force due to each individual multipole mode of the perturbation, and then applies a certain regularization procedure to the mode sum. Here we give the values of all the “regularization parameters” required for implementing this regularization procedure, for any geodesic orbit in Schwarzschild spacetime.