Gravitational scattering, post-Minkowskian approximation, and effective-one-body theory

By T. Damour. 2016

267 citations recorded by the source corpus.

A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small velocities), and employs a new dictionary focussing on the functional dependence of the scattering angle on the total energy and the total angular momentum of the system. Using this approach, we prove to all orders in v/c two results that were previously known to hold only to a limited post-Newtonian accuracy: (i) the relativistic gravitational dynamics of a two-body system is equivalent, at first post-Minkowskian order, to the relativistic dynamics of an effective test particle moving in a Schwarzschild metric; and (ii) this equivalence requires the existence of an exactly quadratic map between the real (relativistic) two-body energy and the (relativistic) energy of the effective particle. The same energy map is also shown to apply to the effective one-body description of two masses interacting via tensor-scalar gravity.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/97a7263700f31716d0cf6c075de250ad3ce29c75

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In Astronomy and Astrophysics

1. T. Damour
2. R. Russo
3. Paolo Di Vecchia
4. R. Roiban
5. M. Zeng
6. Z. Bern
7. Chia-Hsien Shen
8. G. Veneziano

Citations in the corpus

• Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes (2019, methodology): “The technique of deriving the relativistic interaction of two massive objects from an amplitude approach has recently attracted renewed attention [9, 10, 11, 12, 13, 14, 15, 16] since it links directly to the post-Minkowskian approximation of the classical gravitational dynamics relevant for the ins”
• Classical and quantum scattering in post-Minkowskian gravity (2019, methodology): “17)) was already used in [46] to show that the 1PM dynamics is equivalent (after using the EOB energy map) to geodesic motion in a linearized Schwarzschild metric of massM = m1+m2.”
• Black hole binary dynamics from the double copy and effective theory (2019, background): “[9, 33] the scattering angle is a useful stepping stone to obtain an effective one body Hamiltonian [2].”
• Radiation reaction from soft theorems (2021, methodology): “…the study of the inspiral phase of black-hole binaries since it can be used to determine the parameters of the Effective-One-Body description (see [1] and references therein). this reason, gravitational scattering has been at the centre of renewed attention and has been recently investigated…”
• Radiative contribution to classical gravitational scattering at the third order in G (2020, methodology): “[3, 7] (1PM) and Refs.”