Self-force Regularization in the Schwarzschild Spacetime

TL;DR

This paper reviews the challenges and recent progress in calculating the gravitational self-force on particles in Schwarzschild spacetime, focusing on regularization and gauge issues crucial for modeling black hole-particle systems.

Contribution

It provides a detailed discussion of the regularization and gauge problems in self-force calculations and reports recent advances in the Schwarzschild background.

Findings

Progress in regularizing the divergent self-force.

Insights into gauge transformation issues.

Advances in applying self-force calculations to Schwarzschild spacetime.

Abstract

We discuss the gravitational self-force on a particle in a black hole space-time. For a point particle, the full (bare) self-force diverges. The metric perturbation induced by a particle can be divided into two parts, the direct part (or the S part) and the tail part (or the R part), in the harmonic gauge, and the regularized self-force is derived from the R part which is regular and satisfies the source-free perturbed Einstein equations. But this formulation is abstract, so when we apply to black hole-particle systems, there are many problems to be overcome in order to derive a concrete self-force. These problems are roughly divided into two parts. They are the problem of regularizing the divergent self-force, i.e., ``subtraction problem'' and the problem of the singularity in gauge transformation, i.e., ``gauge problem''. In this paper, we discuss these problems in the Schwarzschild background and report some recent progress.