Gravitational multipole moments from Noether charges

TL;DR

This paper introduces a new way to define gravitational multipole moments using Noether charges, aligning with classical definitions in Einstein gravity and providing a framework for analyzing radiative configurations.

Contribution

It establishes a general definition of gravitational multipole moments via Noether charges applicable to any gravity theory, matching known results in Einstein gravity and linking source and radiative multipole moments.

Findings

Definition matches Thorne's moments in Einstein gravity

Total multipole charges include source and radiation contributions

Conservation laws relate source moments to flux at null infinity

Abstract

We define the mass and current multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We show that our definition exactly matches Thorne's mass and current multipole moments in Einstein gravity, which are defined in terms of metric components. For radiative configurations, the total multipole charges -- including the contributions from the source and the radiation -- are given by surface charges at spatial infinity, while the source multipole moments are naturally identified by surface integrals in the near-zone or, alternatively, from a regularization of the Noether charges at null infinity. The conservation of total multipole charges is used to derive the variation of source multipole moments in the near-zone in terms of the flux of multipole charges at null infinity.