Classical Gravitational Self-Energy from Double Copy

TL;DR

This paper extends the classical double copy method to compute the gravitational self-energy of composite systems with multipolar coupling, revealing insights into tail processes and advancing the use of double copy in gravitational dynamics.

Contribution

It generalizes color to kinematics replacement rules for self-energy calculations, enabling systematic analysis of tail processes in two-body gravitational systems.

Findings

Derived next-to-leading order gravitational self-energy results.

Identified tail processes as radiation scattering and re-absorption.

Progressed towards systematic double copy application in multipolar expansions.

Abstract

We apply the classical double copy to the calculation of self-energy of composite systems with multipolar coupling to gravitational field, obtaining next-to-leading order results in the gravitational coupling $G_N$ by generalizing color to kinematics replacement rules known in literature. When applied to the multipolar description of the two-body system, the self-energy diagrams studied in this work correspond to tail processes, whose physical interpretation is of radiation being emitted by the non-relativistic source, scattered by the curvature generated by the binary system and then re-absorbed by the same source. These processes contribute to the conservative two-body dynamics and the present work represents a decisive step towards the systematic use of double copy within the multipolar post-Minkowskian expansion.