Access by Xinjiang University

Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

¹Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, I-00185 Rome, Italy
²Institut des Hautes Etudes Scientifiques, 91440 Bures-sur-Yvette, France

Phys. Rev. D 89, 104047 – Published 23 May, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.104047

Abstract

We analytically compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler’s gauge-invariant redshift variable. We emphasize the increase in “transcendentality” of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of $ζ (3)$ (as well as the square of Euler’s constant $γ$ ) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter $u = G M / (c^{2} r)$ leaves the weak-field domain $u ≪ 1$ to enter the strong field domain $u = O (1)$ .

Article Text

References (28)

D. Bini and T. Damour, Phys. Rev. D 87, 121501(R) (2013).
D. Bini and T. Damour, Phys. Rev. D 89, 064063 (2014).
A. Buonanno and T. Damour, Phys. Rev. D 59, 084006 (1999).
A. Buonanno and T. Damour, Phys. Rev. D 62, 064015 (2000).
T. Damour, P. Jaranowski, and G. Schaefer, Phys. Rev. D 62, 084011 (2000).
T. Damour, Phys. Rev. D 64, 124013 (2001).
S. L. Detweiler, Phys. Rev. D 77, 124026 (2008).
S. Mano, H. Suzuki, and E. Takasugi, Prog. Theor. Phys. 95, 1079 (1996).
S. Mano, H. Suzuki, and E. Takasugi, Prog. Theor. Phys. 96, 549 (1996).
S. Mano and E. Takasugi, Prog. Theor. Phys. 97, 213 (1997).
L. Barack and A. Ori, Phys. Rev. D 61, 061502 (2000).
W. Hikida, H. Nakano, and M. Sasaki, Classical Quantum Gravity 22, S753 (2005).
W. Hikida, S. Jhingan, H. Nakano, N. Sago, M. Sasaki, and T. Tanaka, Prog. Theor. Phys. 113, 283 (2005).
A. Le Tiec, L. Blanchet, and B. F. Whiting, Phys. Rev. D 85, 064039 (2012).
A. Le Tiec, E. Barausse, and A. Buonanno, Phys. Rev. Lett. 108, 131103 (2012).
E. Barausse, A. Buonanno, and A. Le Tiec, Phys. Rev. D 85, 064010 (2012).
T. Damour, Phys. Rev. D 81, 024017 (2010).
L. Blanchet, S. L. Detweiler, A. Le Tiec, and B. F. Whiting, Phys. Rev. D 81, 084033 (2010).
A. G. Shah, J. L. Friedman, and B. F. Whiting, Phys. Rev. D 89, 064042 (2014).
T. Damour, P. Jaranowski, and G. Schfer, Phys. Rev. D 89, 064058 (2014).
S. Akcay, L. Barack, T. Damour, and N. Sago, Phys. Rev. D 86, 104041 (2012).
L. Blanchet, S. L. Detweiler, A. Le Tiec, and B. F. Whiting, Phys. Rev. D 81, 064004 (2010).
L. Barack and N. Sago, Phys. Rev. Lett. 102, 191101 (2009).
T. Damour and G. Esposito-Farese, Phys. Rev. D 53, 5541 (1996).
T. Damour, P. Jaranowski, and G. Schaefer, Phys. Lett. B 513, 147 (2001).
D. J. Broadhurst and D. Kreimer, Int. J. Mod. Phys. C 06, 519 (1995).
F. C. S. Brown, arXiv:0910.0114.
T. Damour, A. Nagar, and S. Bernuzzi, Phys. Rev. D 87, 084035 (2013).

Physical Review D

Export citation

Export citation

Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

Abstract

Article Text

References (28)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation