Metric reconstruction from celestial multipoles
Geoffrey Compère, Roberto Oliveri, Ali Seraj
TL;DR
This work shows that vacuum spacetimes with no incoming radiation can be completely characterized by celestial charges that organize into two infinite multipole towers linked to the Landau-type gravitational duality. By combining post-Minkowskian methods in de Donder gauge with Bondi expansions, the authors derive local flux-balance laws and define two families of celestial charges that reproduce soft theorems and memory effects, while connecting them to the canonical multipole moments. They demonstrate a non-linear gravitational electric-magnetic duality that rotates multipoles and extends to the full non-linear solution space, preserving the symplectic structure. In non-radiative regions, a complete set of conserved quantities is identified, including Geroch-Hansen multipoles, generalized BMS charges, and higher $n\ge2$ celestial multipoles, which together encode all stationary and memory features of the spacetime and enable holographic metric reconstruction outside sources in multiple gauges.
Abstract
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.