2013

High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations

Bini, Donato, Damour, Thibault

Understand

We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us.

This extension is done to linear order in the mass ratio 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.
By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the 6th post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms).
In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.

Built on

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Similar

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1999
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2000
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2001
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S. L. Detweiler, E. Messaritaki and B. F. Whiting, “Selfforce of a scalar field for circular orbits about a Schwarzschild black hole,” Phys. Rev. D 67
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2003
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2004
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Then

S. L. Detweiler, “A Consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry,” Phys. Rev. D 77
Original
2008
Later among the works it cites.
N. Sago, L. Barack and S. L. Detweiler, “Two approaches for the gravitational self force in black hole spacetime: Comparison of numerical results,” Phys. Rev. D 78
Original
2008
Later among the works it cites.
T. Ledvinka, G. Schäfer and J. Bicak, “Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation,” Phys. Rev. Lett. 100
Original
2008
Later among the works it cites.
L. Blanchet, S. L. Detweiler, A. Le Tiec and B. F. Whiting, “High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry,” Phys. Rev. D 81
Original
2010
Later among the works it cites.
T. Damour, 2010, unpublished; cited in L. Barack, T. Damour and N. Sago, “Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism,” Phys. Rev. D 82
Original
2010
Later among the works it cites.
T. Damour, “Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism,” Phys. Rev. D 81
Original
2010
Later among the works it cites.
L. Blanchet, S. L. Detweiler, A. Le Tiec and B. F. Whiting, “Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry,” Phys. Rev. D 81
Original
2010
Later among the works it cites.
W. D. Goldberger and A. Ross, “Gravitational radiative corrections from effective field theory,” Phys. Rev. D 81
Original
2010
Later among the works it cites.
E. Barausse, A. Buonanno and A. Le Tiec, “The complete non-spinning effective-one-body metric at linear order in the mass ratio,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
A. Le Tiec, L. Blanchet and B. F. Whiting, “The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory,” Phys. Rev. D 85
Original
2012
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A. Le Tiec, E. Barausse and A. Buonanno, “Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems,” Phys. Rev. Lett. 108
Original
2012
Later among the works it cites.
S. Akcay, L. Barack, T. Damour and N. Sago, “Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring,” Phys. Rev. D 86
Original
2012
Later among the works it cites.
P. Jaranowski and G. Schafer, “Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems,” Phys. Rev. D 86
Original
2012
Later among the works it cites.
D. Bini and T. Damour, “Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation,” Phys. Rev. D 87
Original
2013
Closest in time.
P. Jaranowski and G. Schäfer, “Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian,” Phys. Rev. D 87
Original
2013
Closest in time.
S. Foffa, “Gravitating binaries at 5PN in the post-Minkowskian approximation,” Phys. Rev. D 89
Original
2014
Closest in time.

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