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Comparison between self-force and post-Newtonian dynamics: Beyond circular orbits

Comparison between self-force and post-Newtonian dynamics: Beyond circular orbits
Comparison between self-force and post-Newtonian dynamics: Beyond circular orbits
The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modeling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a crucial test for both methods and can be used to enhance their accuracy, e.g. via the determination of previously unknown PN parameters. Here, for the first time, we extend such comparisons to noncircular orbits—specifically, to a system of two nonspinning objects in a bound (eccentric) orbit. To enable the comparison we use a certain orbital-averaged quantity ⟨U⟩ that generalizes Detweiler’s redshift invariant. The functional relationship ⟨U⟩(Ωr,Ωϕ), where Ωr and Ωϕ are the frequencies of the radial and azimuthal motions, is an invariant characteristic of the conservative dynamics. We compute ⟨U⟩(Ωr,Ωϕ) numerically through linear order in the mass ratio q, using a GSF code which is based on a frequency-domain treatment of the linearized Einstein equations in the Lorenz gauge. We also derive ⟨U⟩(Ωr,Ωϕ) analytically through 3PN order, for an arbitrary q, using the known near-zone 3PN metric and the generalized quasi-Keplerian representation of the motion. We demonstrate that the O(q) piece of the analytical PN prediction is perfectly consistent with the numerical GSF results, and we use the latter to estimate yet unknown pieces of the 4PN expression at O(q).
1550-7998
1-32
Akcay, Sarp
cf302930-31a9-45e5-94f0-a9cac408e01b
Le Tiec, Alexandre
5d68182b-445c-454b-9c38-627c1788515a
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Sago, Norichika
c4baa9a1-e4fb-448e-8818-f7d189ed2773
Warburton, Niels
88d3f12e-d930-438d-bb54-071292b0c1dc
Akcay, Sarp
cf302930-31a9-45e5-94f0-a9cac408e01b
Le Tiec, Alexandre
5d68182b-445c-454b-9c38-627c1788515a
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Sago, Norichika
c4baa9a1-e4fb-448e-8818-f7d189ed2773
Warburton, Niels
88d3f12e-d930-438d-bb54-071292b0c1dc

Akcay, Sarp, Le Tiec, Alexandre, Barack, Leor, Sago, Norichika and Warburton, Niels (2015) Comparison between self-force and post-Newtonian dynamics: Beyond circular orbits. Physical Review D, 91, 1-32. (doi:10.1103/PhysRevD.91.124014).

Record type: Article

Abstract

The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modeling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a crucial test for both methods and can be used to enhance their accuracy, e.g. via the determination of previously unknown PN parameters. Here, for the first time, we extend such comparisons to noncircular orbits—specifically, to a system of two nonspinning objects in a bound (eccentric) orbit. To enable the comparison we use a certain orbital-averaged quantity ⟨U⟩ that generalizes Detweiler’s redshift invariant. The functional relationship ⟨U⟩(Ωr,Ωϕ), where Ωr and Ωϕ are the frequencies of the radial and azimuthal motions, is an invariant characteristic of the conservative dynamics. We compute ⟨U⟩(Ωr,Ωϕ) numerically through linear order in the mass ratio q, using a GSF code which is based on a frequency-domain treatment of the linearized Einstein equations in the Lorenz gauge. We also derive ⟨U⟩(Ωr,Ωϕ) analytically through 3PN order, for an arbitrary q, using the known near-zone 3PN metric and the generalized quasi-Keplerian representation of the motion. We demonstrate that the O(q) piece of the analytical PN prediction is perfectly consistent with the numerical GSF results, and we use the latter to estimate yet unknown pieces of the 4PN expression at O(q).

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More information

Published date: 3 June 2015
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 408695
URI: https://eprints.soton.ac.uk/id/eprint/408695
ISSN: 1550-7998
PURE UUID: 66a93f27-e8ab-4160-b2d8-744f87fd5e3d

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Date deposited: 26 May 2017 04:02
Last modified: 13 Mar 2019 19:54

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