A New Gauge for Asymptotically Flat Spacetime

TL;DR

This paper introduces a novel gauge for asymptotically flat spacetime that treats future and past null infinities equally, enabling a better understanding of the gravitational S-matrix and BMS symmetries.

Contribution

It proposes a new gauge that symmetrically handles null infinities and reveals the diagonal BMS symmetry from asymptotic CPT invariance.

Findings

Finite BMS charges at null infinities.

Emergence of diagonal BMS$^0$ symmetry.

Potential for holographic renormalization.

Abstract

We present a new gauge for asymptotically flat spacetime that can treat future and past null infinities ($\mathscr{I}^{+}$ or $\mathscr{I}^{-}$) democratically. Our gauge is complementary to Bondi and Ashtekar-Hansen gauges, and is adapted to the $S$-matrix being the natural observable. One new feature is that the holographic directions are null. We present a set of consistent fall-offs in terms of null coordinates at $\mathscr{I}^{+}$ and $\mathscr{I}^{-}$, with finite BMS$^{\pm}$ charges. The diagonal BMS$^0$ symmetry of the gravitational $S$-matrix emerges upon demanding {\em asymptotic} CPT invariance. Trivial diffeomorphisms, (absence of) log fall-offs, possible enhancements of BMS algebra, and the possibility of holographic renormalization of data at $\mathscr{I}^{+}_-$ and $\mathscr{I}^{-}_+$, play interesting roles. Gory details of the various new technical features that emerge, are elaborated in a companion paper to this letter.