Prog. Theor. Phys. Vol. 113 No. 2 (2005) pp. 283-303

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A New Analytical Method for Self-Force Regularization. II

— Testing the Efficiency for Circular Orbits —

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

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

(Received November 4, 2004)

Abstract:

In a previous paper, based on the black hole perturbation approach, we formulated a new analytical method for regularizing the self-force acting on a particle of small mass µ orbiting a Schwarzschild black hole of mass M, where µ≪M. In our method, we divide the self-force into the \tildeS-part and \tildeR-part. All the singular behavior is contained in the \tilde S-part, and hence the \tildeR-part is guaranteed to be regular. In this paper, focusing on the case of a scalar-charged particle for simplicity, we investigate the precision of both the regularized \tilde S-part and the \tildeR-part required for the construction of sufficiently accurate waveforms for almost circular inspiral orbits. We calculate the regularized \tildeS-part for circular orbits to 18th post-Newtonian (PN) order and investigate the convergence of the post-Newtonian expansion. We also study the convergence of the remaining \tildeR-part in the spherical harmonic expansion. We find that a sufficiently accurate Green function can be obtained by keeping the terms up to ℓ= 13.

URL : http://ptp.ipap.jp/link?PTP/113/283/
DOI : 10.1143/PTP.113.283

^*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@vega.ess.sci.osaka-u.ac.jp
^*****E-mail: misao@yukawa.kyoto-u.ac.jp
^******E-mail: tama@scphys.kyoto-u.ac.jp

References:

B. Abbot et al., Nucl. Instrum. Methods A 517 (2004), 154.
LIGO web page: http://www.ligo.caltech.edu/
R. Takahashi and the TAMA Collaboration, Class. Quantum Grav. 21 (2004), S403[CrossRef].
TAMA300 web page: http://tamago.mtk.nao.ac.jp/
B. Willke et al., Class. Quantum Grav. 21 (2004), S417[CrossRef].
GEO600 web page: http://www.geo600.uni-hannover.de/
F. Acernese et al., Class. Quantum Grav. 21 (2004), S385[CrossRef].
VIRGO web page: http://www.virgo.infn.it/
LISA web page: http://lisa.jpl.nasa.gov/
N. Seto, S. Kawamura and T. Nakamura, Phys. Rev. Lett. 87 (2001), 221103[APS].
BBO web page: http://universe.gsfc.nasa.gov/program/bbo.html
Luc Blanchet, Living Rev. Relativity 5 (2002), 3.
For a review, see e.g., Y. Mino, M. Sasaki, M. Shibata, T. Tagoshi and T. Tanaka, Prog. Theor. Phys. Suppl. No. 128 (1997), 1[PTP].
M. Sasaki and H. Tagoshi, Living Rev. Relativity 6 (2003), 6.
B. S. DeWitt and R. W. Brehme, Ann. of Phys. 9 (1960), 220[CrossRef].
Y. Mino, M. Sasaki and T. Tanaka, Phys. Rev. D 55 (1997), 3457[APS].
T. C. Quinn and R. M. Wald, Phys. Rev. D 56 (1997), 3381[APS].
S. Detweiler and B. F. Whiting, Phys. Rev. D 67 (2003), 024025[APS].
L. Barack and A. Ori, gr-qc/9911040[e-print arXiv].
L. M. Burko, Class. Quantum Grav. 17 (2000), 227[CrossRef].
L. M. Burko, gr-qc/9911089[e-print arXiv].
L. Barack and A. Ori, Phys. Rev. D 61 (2000), 061502[APS](R).
L. M. Burko, Phys. Rev. Lett. 84 (2001), 4529[APS].
L. Barack, Phys. Rev. D 62 (2000), 084027[APS].
L. Barack and L. M. Burko, Phys. Rev. D 62 (2000), 084040[APS].
L. M. Burko, Y. T. Liu and Y. Soen, Phys. Rev. D 63 (2001), 024015[APS].
H. Nakano, Y. Mino and M. Sasaki, Prog. Theor. Phys. 106 (2001), 339[PTP].
L. Barack and A. Ori, Phys. Rev. D 66 (2002), 084022[APS].
S. Detweiler, E. Messaritaki and B. F. Whiting, Phys. Rev. D 67 (2003), 104016[APS].
M. Diaz-Rivera, E. Messaritaki, B. F. Whiting and S. Detweiler, gr-qc/0410011[e-print arXiv].
W. Hikida, S. Jhingan, H. Nakano, N. Sago, M. Sasaki and T. Tanaka, Prog. Theor. Phys. 111 (2004), 821[PTP].
L. Barack, Y. Mino, H. Nakano, A. Ori and M. Sasaki, Phys. Rev. Lett. 88 (2002), 091101[APS].
Y. Mino, H. Nakano and M. Sasaki, Prog. Theor. Phys. 108 (2003), 1039[PTP].
L. Barack and A. Ori, Phys. Rev. D 67 (2003), 024029[APS].
L. Barack and A. Ori, Phys. Rev. Lett. 90 (2003), 111101[APS].
A. Wiseman, Phys. Rev. D 61 (2001), 084014[APS].
S. Mano, H. Suzuki and E. Takasugi, Prog. Theor. Phys. 95 (1996), 1079[PTP]; Prog. Theor. Phys. 96 (1996), 549[PTP].
S. Mano and E. Takasugi, Prog. Theor. Phys. 97 (1997), 213[PTP].
R. Fujita and H. Tagoshi, private communication.
A. Ori and K. S. Thorne, Phys. Rev. D 62 (2000), 124022[APS].

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