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Charge and Antipodal Matching across Spatial Infinity

Federico Capone, Kevin Nguyen, Enrico Parisini

Abstract

We derive the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end we provide a precise map between Bondi data at null infinity $\mathscr{I}$ and Beig-Schmidt data at spatial infinity $i^0$ in a context appropriate to the gravitational scattering problem and celestial holography. In addition, we explicitly match the various proposals of BMS charges at $\mathscr{I}$ found in the literature with the conserved charges at $i^0$.

Charge and Antipodal Matching across Spatial Infinity

Abstract

We derive the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end we provide a precise map between Bondi data at null infinity and Beig-Schmidt data at spatial infinity in a context appropriate to the gravitational scattering problem and celestial holography. In addition, we explicitly match the various proposals of BMS charges at found in the literature with the conserved charges at .
Paper Structure (27 sections, 127 equations)

This paper contains 27 sections, 127 equations.

Table of Contents

  1. Introduction
  2. Conventions.
  3. Gravity at null infinity
  4. Gravity at spatial infinity
  5. Leading fields.
  6. Subleading field.
  7. From Bondi to Beig-Schmidt
  8. Antipodal matching relations
  9. Harmonic and Legendre functions.
  10. Mass aspect.
  11. Shear tensor.
  12. Matching of BMS charges from $\mathscr{I}$ to $i^0$
  13. BMS charges at $\mathscr{I}^+_-$.
  14. Supertranslation charges.
  15. Lorentz charges.
  16. ...and 12 more sections