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Numerical computation of the effective-one-body potential q using self-force results

Numerical computation of the effective-one-body potential q using self-force results
Numerical computation of the effective-one-body potential q using self-force results
The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two nonspinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: a(v), d¯(v), q(v). By generalizing the first law of mechanics for (nonspinning) black hole binaries to eccentric orbits, [A. Le Tiec, Phys. Rev. D 92, 084021 (2015).] recently obtained new expressions for d¯(v) and q(v) in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential q(v) by combining results from two independent numerical self-force codes. We determine q(v) for inverse binary separations in the range 1/1200?v?1/6. Our computation thus provides the first-ever strong-field results for q(v). We also obtain d¯(v) in our entire domain to a fractional accuracy of ?10-8. We find that our results are compatible with the known post-Newtonian expansions for d¯(v) and q(v) in the weak field, and agree with previous (less accurate) numerical results for d¯(v) in the strong field.
1550-7998
1-17
Akcay, Sarp
fa1e3ced-9bdf-41b0-b5b7-777f114d753d
Van De Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22
Akcay, Sarp
fa1e3ced-9bdf-41b0-b5b7-777f114d753d
Van De Meent, Maarten
c06e1d53-18af-4ef1-8671-ff99b1a1df22

Akcay, Sarp and Van De Meent, Maarten (2016) Numerical computation of the effective-one-body potential q using self-force results. Physical Review D, 93 (64063), 1-17. (doi:10.1103/PhysRevD.93.064063).

Record type: Article

Abstract

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two nonspinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: a(v), d¯(v), q(v). By generalizing the first law of mechanics for (nonspinning) black hole binaries to eccentric orbits, [A. Le Tiec, Phys. Rev. D 92, 084021 (2015).] recently obtained new expressions for d¯(v) and q(v) in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential q(v) by combining results from two independent numerical self-force codes. We determine q(v) for inverse binary separations in the range 1/1200?v?1/6. Our computation thus provides the first-ever strong-field results for q(v). We also obtain d¯(v) in our entire domain to a fractional accuracy of ?10-8. We find that our results are compatible with the known post-Newtonian expansions for d¯(v) and q(v) in the weak field, and agree with previous (less accurate) numerical results for d¯(v) in the strong field.

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Published date: 25 March 2016
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 397865
URI: http://eprints.soton.ac.uk/id/eprint/397865
ISSN: 1550-7998
PURE UUID: b1445057-434d-4037-aae7-47f3e431044b

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Date deposited: 08 Jul 2016 10:40
Last modified: 09 Dec 2019 19:33

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