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arXiv · gr-qc/0010036

Gravitational reaction force on a particle in the Schwarzschild background

Hiroyuki Nakano·Misao Sasaki
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Abstract

We formulate a new method to calculate the gravitational reaction force on a particle of mass $μ$ orbiting a massive black hole of mass $M$. In this formalism, the tail part of the retarded Green function, which is responsible for the reaction force, is calculated at the level of the Teukolsky equation. Our method naturally allows a systematic post-Minkowskian (PM) expansion of the tail part at short distances. As a first step, we consider the case of a Schwarzschild black hole and explicitly calculate the first post-Newtonian (1PN) tail part of the Green function. There are, however, a couple of issues to be resolved before explicitly evaluating the reaction force by applying the present method. We discuss possible resolutions of these issues.

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Hiroyuki Nakano, Misao Sasaki. 2001-01-17. Gravitational reaction force on a particle in the Schwarzschild background. https://doi.org/10.1143/ptp.105.197

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