Prog. Theor. Phys. Vol. 108 No. 6 (2002) pp. 1039-1064

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

— Mode Decomposition Regularization —

Yasushi Mino,^1,^* Hiroyuki Nakano^2,^** and Misao Sasaki^2,^***

¹Department of Physics, Washington University, Campus Box 1105, One Brookings Dr., St. Louis, MO 63130-4899, USA
²Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan

(Received August 1, 2002)

Abstract:

The covariant structure of the self-force of a particle in a general curved background has been elucidated in the cases of scalar, electromagnetic, and gravitational charges. Specifically, what we need is the part of the self-field that is non-vanishing off and within the past light cone of the particle's location, the so-called tail. The radiation reaction force in the absence of external fields is entirely contained in the tail. In this paper, we develop the mathematical tools necessary for the regularization and propose a practical method to calculate the self-force of a particle orbiting a Schwarzschild black hole.

URL : http://ptp.ipap.jp/link?PTP/108/1039/
DOI : 10.1143/PTP.108.1039

^*E-mail: mino@wugrav.wustl.edu
^**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) :

Progress of Theoretical Physics Vol. 111 No. 6 (2004) pp. 821-840 :
A New Analytical Method for Self-Force Regularization. I

Wataru Hikida, Sanjay Jhingan, Hiroyuki Nakano, Norichika Sago, Misao Sasaki, and Takahiro Tanaka
Progress of Theoretical Physics Vol. 113 No. 2 (2005) pp. 283-303 :
A New Analytical Method for Self-Force Regularization. II

Wataru Hikida, Sanjay Jhingan, Hiroyuki Nakano, Norichika Sago, Misao Sasaki and Takahiro Tanaka
Progress of Theoretical Physics Vol. 113 No. 4 (2005) pp. 733-761 :
Self-Force in the Radiation Reaction Formula

Yasushi Mino
Progress of Theoretical Physics Vol. 117 No. 6 (2007) pp. 1041-1066 :
Adiabatic Evolution of Three `Constants' of Motion for Greatly Inclined Orbits in Kerr Spacetime

Katsuhiko Ganz, Wataru Hikida, Hiroyuki Nakano, Norichika Sago and Takahiro Tanaka
Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145 :
Gravitational Radiation Reaction

Takahiro Tanaka