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Prog. Theor. Phys. Vol. 111 No. 6 (2004) pp. 821-840

[ Full Text PDF : FREE ACCESS (224K) ]

A New Analytical Method for Self-Force Regularization. I

— Charged Scalar Particles in Schwarzschild Spacetime —

Wataru Hikida,1,* Sanjay Jhingan,2,** Hiroyuki Nakano,3,*** Norichika Sago,4,5,**** Misao Sasaki,1,***** and Takahiro Tanaka4,******

1Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
2Departamento de Física Teórica, Universidad del País Vasco, Apdo. 644, 48080, Bilbao, Spain
3Department of Mathematics and Physics, Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
4Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
5Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka 560-0043, Japan

(Received March 3, 2004)

Abstract:

We formulate a new analytical method for regularizing the self-force acting on a particle of small mass µ orbiting a black hole of mass M, where µ≪M. At first order in µ, the geometry is perturbed and the motion of the particle is affected by its self-force. The self-force, however, diverges at the location of the particle, and hence should be regularized. It is known that a properly regularized self-force is given by the tail part (or the R-part) of the self-field, obtained by subtracting the direct part (or the S-part) from the full self-field. The most successful method of regularization proposed so far relies on the spherical harmonic decomposition of the self-force, the so-called mode-sum regularization or mode decomposition regularization. However, except for some special orbits, no systematic analytical method for computing the regularized self-force has been constructed. In this paper, utilizing a new decomposition of the retarded Green function in the frequency domain, we formulate a systematic method for the computation of the self-force in the time domain. Our method relies on the post-Newtonian (PN) expansion, but the order of the expansion can be arbitrarily high. To demonstrate the essence of our method, in this paper, we focus on a scalar charged particle on the Schwarzschild background. Generalization to the gravitational case is straightforward, except for some subtle issues related with the choice of gauge (which exists irrespective of regularization methods).


URL : http://ptp.ipap.jp/link?PTP/111/821/
DOI : 10.1143/PTP.111.821


*E-mail: hikida@yukawa.kyoto-u.ac.jp
**E-mail: wtpsaxxj@lg.ehu.es
***E-mail: denden@sci.osaka-cu.ac.jp
****E-mail: sago@tap.scphys.kyoto-u.ac.jp
*****E-mail: misao@yukawa.kyoto-u.ac.jp
******E-mail: tama@scphys.kyoto-u.ac.jp

[ Full Text PDF : FREE ACCESS (224K) ] Citation:

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Citing Article(s) :

  1. 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
  2. Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145 :
    Gravitational Radiation Reaction
    Takahiro Tanaka

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