Calculating the gravitational self force in Schwarzschild spacetime

TL;DR

This paper introduces a practical mode-sum regularization method for calculating the local gravitational self-force on a particle orbiting a Schwarzschild black hole, providing all necessary parameters for implementation.

Contribution

It provides explicit regularization parameters for mode-sum regularization applicable to any geodesic orbit in Schwarzschild spacetime.

Findings

Derived all regularization parameters for mode-sum method

Enables practical computation of self-force in Schwarzschild spacetime

Facilitates more accurate modeling of particle dynamics near black holes

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 {\it 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.