Mode sum regularization approach for the self-force in black hole spacetime

TL;DR

This paper introduces a mode sum regularization method to compute the self-force on a scalar charge in Schwarzschild black hole spacetime, enabling more accurate modeling of particle dynamics in strong gravitational fields.

Contribution

The paper develops a new regularization procedure for mode sum calculations of the self-force on a scalar charge in Schwarzschild spacetime, including implementation for radial trajectories.

Findings

Regularization procedure successfully applied to scalar charge in Schwarzschild background.

Method enables calculation of self-force for non-geodesic radial trajectories.

Provides a foundation for more precise self-force computations in black hole physics.

Abstract

We present a method for calculating the self-force (the ``radiation reaction force'') acting on a charged particle moving in a strong field orbit in black hole spacetime. In this approach, one first calculates the contribution to the self-force due to each multipole mode of the particle's field. Then, the sum over modes is evaluated, subject to a certain regularization procedure. Here we develop this regularization procedure for a scalar charge on a Schwarzschild background, and present the results of its implementation for radial trajectories (not necessarily geodesic).