In this paper, we propose a new method to extract the singular part from the linear metric perturbation induced by a point particle moving on a Schwarzschild/Kerr black hole. The only assumption we make is a kind of analiticity of the resulting metric perturbation around the particle. The method is expected to be useful in investigating the gravitational radiation reaction to the motion of the particle, its spin, and so on.
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Mino et al. (1998) studied this question.