---

Prog. Theor. Phys. Vol. 106 No. 2 (2001) pp. 339-362

Self-Force on a Scalar Charge in Circular Orbit around a Schwarzschild Black Hole

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

Department of Earth and Space Science, Graduate School of Science
Osaka University, Toyonaka 560-0043, Japan
^*Theoretical Astrophysics, California Institute of Technology
Pasadena, California 91125, USA

(Received April 12, 2001)

Abstract:

In an accompanying paper, we formulate two types of regularization methods to calculate the scalar self-force on a particle of charge q moving around a black hole of mass M [Y. Mino, H. Nakano and M. Sasaki, Covariant Self-force Regularization of a Particle Orbiting a Schwarzschild Black Hole, UTAP-386, OUTAP-157 (2001)], one of which is called the “power expansion regularization”. In this paper, we analytically evaluate the self-force (which we also call the `reaction force') to third post-Newtonian (3PN) order for a scalar particle in circular orbit around a Schwarzschild black hole by using the power expansion regularization. It is found that the r-component of the self-force arises at 3PN order, whereas the t- and φ-components, which are due to the radiation reaction, appear at 2PN and 1.5PN orders, respectively.

URL : http://ptp.ipap.jp/link?PTP/106/339/
DOI : 10.1143/PTP.106.339

^* E-mail: denden@vega.ess.sci.osaka-u.ac.jp
^** E-mail: mino@utap.phys.s.u-tokyo.ac.jp (on the leave from University of Tokyo)
^***E-mail: misao@vega.ess.sci.osaka-u.ac.jp

[ Full Text PDF (220K) ]  [ Buy This Article ]  Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. Y. Mino, H. Nakano and M. Sasaki, Covariant Self-force Regularization of a Particle Orbiting a Schwarzschild Black Hole, UTAP-386, OUTAP-157 (2001).
2. LIGO web page: http://www.ligo.caltech.edu/
3. VIRGO web page: http://www.virgo.infn.it/
4. GEO600 web page: http://www.geo600.uni-hannover.de/
5. TAMA300 web page: http://tamago.mtk.nao.ac.jp/
6. LISA web page: http://lisa.jpl.nasa.gov/
7. Y. Mino, M. Sasaki, M. Shibata, H. Tagoshi and T. Tanaka, Prog. Theor. Phys. Suppl. No. 128 (1997), 1[IPAP].
8. B. Carter, Phys. Rev. 174 (1968), 1559[APS]; Commun. Math. Phys. 10 (1968), 280.
9. Y. Mino, M. Sasaki and T. Tanaka, Phys. Rev. D 55 (1997), 3457[APS]; Prog. Theor. Phys. Suppl. No. 128 (1997), 373[IPAP].
10. T. C. Quinn and R. M. Wald, Phys. Rev. D 56 (1997), 3381[APS]; 60 (1999), 064009.
11. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale University Press, New Haven, 1923).
12. B. S. DeWitt and R. W. Brehme, Ann. of Phys. 9 (1960), 220[CrossRef].
13. P. L. Chrzanowski, Phys. Rev. D 11 (1975), 2042[APS].
14. S. A. Teukolsky, Astrophys. J. 185 (1973), 635[CrossRef].
15. Y. Mino, Prog. Theor. Phys. 99 (1998), 79[IPAP].
16. Y. Mino and H. Nakano, Prog. Theor. Phys. 100 (1998), 507[IPAP].
17. H. Nakano and M. Sasaki, Prog. Theor. Phys. 205 (2001), 197, [IPAP] gr-qc/0010036[e-print arXiv].
18. S. Mano, H. Suzuki and E. Takasugi, Prog. Theor. Phys. 95 (1996), 1079[IPAP]; 96 (1996), 549.
19. S. Mano and E. Takasugi, Prog. Theor. Phys. 97 (1997), 213[IPAP].
20. L. Barack and A. Ori, Phys. Rev. D 61 (2000), 061502[APS].
21. L. M. Burko, Phys. Rev. Lett. 84 (2000), 4529[APS]; Class. Quant. Grav. 17 (2000), 227[IoP STACKS].
22. L. Barack and L. M. Burko, Phys. Rev. D 62 (2000), 084040[APS].
23. L. Barack, Phys. Rev. D 62 (2000), 084027[APS].
24. C. O. Lousto, Phys. Rev. Lett. 84 (2000), 5251[APS].
25. L. M. Burko, Y. T. Liu and Y. Soen, Phys. Rev. D 63 (2001), 024015[APS].
26. S. Detweiler, Phys. Rev. Lett. 86 (2001), 1931, [APS] gr-qc/0011039[e-print arXiv].
27. T. C. Quinn, Phys. Rev. D 62 (2000), 064029[APS].
28. P. L. Chrzanowski and C. W. Misner, Phys. Rev. D 10 (1974), 1701[APS].
29. D. V. Gal'tsov, J. of Phys. A 15 (1982), 3737[IoP STACKS].
30. M. Sasaki, Prog. Theor. Phys. 92 (1994), 17[IPAP].
31. E. Poisson and M. Sasaki, Phys. Rev. D 51 (1995), 5753[APS].

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

2. 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

3. 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

4. Progress of Theoretical Physics Supplement No.163 (2006) pp. 120-145 :

   Gravitational Radiation Reaction

   Takahiro Tanaka

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2010 All rights reserved.