Conservative binary dynamics from gravitational tail emission processes

TL;DR

This paper revisits the conservative two-body dynamics in gravitational systems, focusing on tail emission processes and addressing gauge condition violations in amplitude calculations.

Contribution

It identifies and fixes a gauge violation in the calculation of tail contributions to conservative dynamics, linking quantum amplitudes to classical gravitational effects.

Findings

Verification of the correspondence between two-loop self-energy amplitudes and classical emission amplitudes.

Identification of gauge violation due to Lorentz gauge condition in tail process calculations.

Proposal of a fix via an action functional to restore gauge consistency.

Abstract

We re-analyze the far zone contribution to the two-body conservative dynamics arising from interaction between radiative and longitudinal modes, the latter sourced by mass and angular momentum, which in the mass case is known as tail process. We verify the expected correspondence between two loop self-energy amplitudes and the gluing of two classical (one leading order, one at one loop) emission amplitudes. In particular we show that the factorization of the self-energy amplitude involving the angular momentum is violated when applying standard computation procedures, due to a violation of the Lorentz gauge condition commonly adopted in perturbative computations. We show however that a straightforward fix exists, as the violation corresponds to a consistent anomaly, and it can be re-absorbed by the variation of a suitable action functional.