Geometry and Physics of Null Infinity

TL;DR

The paper surveys the geometry and physics of null infinity in asymptotically flat spacetimes, centering on how conformal compactification reveals the BMS symmetry, radiative data, and vacuum structure. It develops the intrinsic phase space of radiative modes, derives the BMS charges via a symplectic momentum map, and then quantizes these modes using a Weyl algebra and a Kahler structure to form asymptotic Fock spaces, shedding light on infrared aspects and soft gravitons. The work highlights the deep link between gravitational radiation, memory effects, and asymptotic symmetries, and discusses extensions and open issues, including the challenge of positive cosmological constant. Overall, it provides a cohesive framework marrying geometric analysis with gravitational physics, spanning classical and quantum regimes at null infinity.

Abstract

In asymptotically Minkowski space-times, one finds a surprisingly rich interplay between geometry and physics in both the classical and quantum regimes. On the mathematical side it involves null geometry, infinite dimensional groups, symplectic geometry on the space of gravitational connections and geometric quantization via Kähler structures. On the physical side, null infinity provides a natural home to study gravitational radiation and its structure leads to several interesting effects such as an infinite dimensional enlargement of the Poincaré group, geometrical expressions of energy and momentum carried by gravitational waves, emergence of non-trivial `vacuum configurations' and an unforeseen interplay between infrared properties of the quantum gravitational field and the enlargement of the asymptotic symmetry group. The goal of this article is to present a succinct summary of this subtle and beautiful interplay.