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Gravitational multipole moments from Noether charges

Research paper by G. Compère, R. Oliveri, A. Seraj

Indexed on: 23 Nov '17Published on: 23 Nov '17Published in: arXiv - High Energy Physics - Theory



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 are used to derive the variation of source multipole moments in terms of the radiative multipole fluxes.