Self-force regularization in the Schwarzschild spacetime

Abstract

We discuss the gravitational self-force on a particle in a black-hole spacetime. 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 Lorenz 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 it 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.