Metric reconstruction from celestial multipoles

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.

v1: 25 pages; v2: text improved, references added, sec.3 "Gravitational electric-magnetic duality" expanded, matches published version in JHEP

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• Symmetries of the gravitational scattering in the absence of peeling
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Gravitational memory effects and higher derivative actions
• Memory effects from holonomies
• Ehlers, Carroll, Charges and Dual Charges
• Higher memory effects and the post-Newtonian calculation of their gravitational-wave signals
• Higher Memory Effects in Numerical Simulations of Binary Black Hole Mergers
• Gyroscopic Gravitational Memory from quasi-circular binary systems
• Gravitational-wave memory effects in the Damour-Esposito-Farèse extension of Brans-Dicke theory
• The Algebraic Structure Underlying Pole-Skipping Points
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Scalar subleading soft theorems from an infinite tower of charges