Metric reconstruction from celestial multipoles

TL;DR

This paper explores how vacuum solutions in Einstein's gravity can be characterized by celestial charges linked to multipole moments, enabling metric reconstruction and revealing dualities and conserved quantities in non-radiative regions.

Contribution

It introduces a comprehensive framework connecting celestial charges, multipole moments, and gravitational dualities, advancing the understanding of non-radiative spacetime structures.

Findings

Spacetimes are characterized by celestial charges including multipole and BMS charges.

Transitions between non-radiative regions are labeled by celestial charges.

The metric can be holographically reconstructed from celestial charges and multipole moments.

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.