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Prog. Theor. Phys. Vol. 105 No. 2 (2001) pp. 197-218

The Gravitational Reaction Force on a Particle in the Schwarzschild Background

Hiroyuki Nakano^*) and Misao Sasaki^**)

Department of Earth and Space Science, Graduate School of Science Osaka University, Toyonaka 560-0043, Japan

(Received October 11, 2000)

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.

URL : http://ptp.ipap.jp/link?PTP/105/197/
DOI : 10.1143/PTP.105.197

^*) E-mail: denden@vega.ess.sci.osaka-u.ac.jp
^**) E-mail: misao@vega.ess.sci.osaka-u.ac.jp

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 108 No. 6 (2002) pp. 1039-1064 :

   Covariant Self-Force Regularization of a Particle Orbiting a Schwarzschild Black Hole

   Yasushi Mino, Hiroyuki Nakano and Misao Sasaki

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