Metric reconstruction from celestial multipoles
Geoffrey Compère (Université Libre de Bruxelles, Centre for Gravitational Waves, International Solvay Institutes, CP 231, Brussels, B-1050, Belgium); Roberto Oliveri (LUTH, Laboratoire Univers et Théories, Observatoire de Paris, CNRS, Université PSL, Université Paris Cité, 5 place Jules Janssen, Meudon, 92190, France); Ali Seraj (Université Libre de Bruxelles, Centre for Gravitational Waves, International Solvay Institutes, CP 231, Brussels, B-1050, Belgium)
The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be mapped into each other under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely characterized by a set of conserved celestial charges that consist of the Geroch-Hansen multipole moments, the generalized BMS charges and additional celestial multipoles accounting for subleading memory effects. Transitions among non-radiative regions, induced by radiative processes, are therefore labelled by celestial charges, which are identified in terms of canonical multipole moments of the linearized gravitational field. The dictionary between celestial charges and canonical multipole moments allows to holographically reconstruct the metric in de Donder, Newman-Unti or Bondi gauge outside of sources.
