Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory

TL;DR

This paper introduces a new Effective One-Body approach for gravitational two-body systems using post-Minkowskian approximation, proving key dynamics equivalences and energy mappings to all orders in velocity.

Contribution

It presents a novel post-Minkowskian based EOB framework with a new scattering angle dependence dictionary, establishing exact energy maps and extending to tensor-scalar gravity.

Findings

Relativistic two-body dynamics is equivalent to an effective test particle in Schwarzschild spacetime at first post-Minkowskian order.

An exact quadratic energy map relates real two-body energy to effective particle energy.

The approach applies to tensor-scalar gravity interactions.

Abstract

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.