A New Gauge for Asymptotically Flat Spacetime

Abstract

We present a new gauge for asymptotically flat spacetime that can treat future and past null infinities (${\mathcal{I}}^{+}$ or ${\mathcal{I}}^{-}$) 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 ${\mathcal{I}}^{+}$ and ${\mathcal{I}}^{-}$, 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 ${\mathcal{I}}_{-}^{+}$ and ${\mathcal{I}}_{+}^{-}$, play interesting roles. Gory details of the various new technical features that emerge, are elaborated in a companion paper to this letter.

arXiv comment5 pages. v2,v3: typos fixed, slight re-wording, refs added, v4: clarifications, speculative comments, author emails and references added