Near and far zone in two-body dynamics: an effective field theory perspective

TL;DR

This paper analyzes the near and far zone interactions in two-body gravitational dynamics using effective field theory, clarifying boundary conditions, divergences, and deriving tail and memory effects in post-Newtonian approximation.

Contribution

It provides a field-theory derivation of tail and memory effects, clarifies boundary conditions, and explores the relation between divergences and emitted power in two-body gravitational systems.

Findings

Rederived far-zone self-energy processes including tail and memory effects.

Clarified the role of boundary conditions in Green's functions.

Generalized divergence calculations to arbitrary post-Newtonian order.

Abstract

We revisit several aspects of the interaction of self-gravitating, slowly varying sources with their own emitted radiation within the context of post-Newtonian approximation to General Relativity. We discuss and clarify the choice of boundary conditions of Green's functions used to determine conservative potentials, and the interplay between the so-called near and far zones, as well as the relation between far zone ultra-violet divergences and emitted power. Both near and far zone contributions are required for the computation of the conservative dynamics. Within a field-theory approach we rederive far-zone self-energy processes, known as tail and memory effects, generalising the calculation of their divergent part to arbitrary order in the post-Newtonian expansion.