Self-force Regularization in the Schwarzschild Spacetime

Details Self-force Regularization in the Schwarzschild Spacetime Self-force Regularization in the Schwarzschild Spacetime

2004-11-30

arxiv.org/abs/gr-qc/0411150v1

Class.Quant.Grav.22:S753-S782,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

34 pages, 2 figures, submitted to CQG, special volume for Radiation Reaction (CAPRA7)

Scientific paper

10.1088/0264-9381/22/15/009

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.

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