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2021

Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity

Damgaard, Poul H., Vanhove, Pierre

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The Effective One-Body formalism of the gravitational two-body problem in general relativity is reconsidered in the light of recent scattering amplitude calculations.

Based on the kinematic relationship between momenta and the effective potential, we consider an energy-dependent effective metric describing the scattering in terms of an Effective One-Body problem for the reduced mass.
The identification of the effective metric simplifies considerably in isotropic coordinates when combined with a redefined angular momentum map.
While the effective energy-dependent metric as expected is not unique, solutions can be chosen perturbatively in the Post-Minkowskian expansion without the need to introduce non-metric corrections.

Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity · Around

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T. Damour, “Coalescence of Two Spinning Black Holes: an Effective One-Body Approach,” Phys. Rev. D 64
2001
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P. Jaranowski and G. Schaefer, “Third Postnewtonian Higher Order Adm Hamilton Dynamics for Two-Body Point Mass Systems,” Phys. Rev. D 57
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A. Cristofoli, P. H. Damgaard, P. Di Vecchia and C. Heissenberg, “Second-order Post-Minkowskian scattering in arbitrary dimensions,” JHEP 07
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2003
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J. Parra-Mart\́frac{i}{2}nez, M. S. Ruf and M. Zeng, “Extremal Black Hole Scattering at 𝒪 ⁡ ( G 3 ) \mathcal{O}(G^{3}) : Graviton Dominance, Eikonal Exponentiation, and Differential Equations,” JHEP 11
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2005
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A. Buonanno, Y. Chen and T. Damour, “Transition from Inspiral to Plunge in Precessing Binaries of Spinning Black Holes,” Phys. Rev. D 74

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J. Vines, “Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings,” Class. Quant. Grav. 35
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2018
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D. A. Kosower, B. Maybee and D. O’Connell, “Amplitudes, Observables, and Classical Scattering,” JHEP 02
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2019
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J. Vines, J. Steinhoff and A. Buonanno, “Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order,” Phys. Rev. D 99
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2019
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P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, “Radiation Reaction from Soft Theorems,” Phys. Lett. B 818
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Z. Bern, J. Parra-Martinez, R. Roiban, M. S. Ruf, C. H. Shen, M. P. Solon and M. Zeng, “Scattering Amplitudes and Conservative Binary Dynamics at 𝒪 ⁡ ( G 4 ) {\cal O}(G^{4}) ,” Phys. Rev. Lett. 126

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