Geometry and Physics of Null Infinity

TL;DR

This paper explores the rich geometric and physical structures at null infinity in asymptotically Minkowski space-times, highlighting their implications for gravitational radiation, symmetries, and quantum aspects.

Contribution

It provides a comprehensive summary of the interplay between null geometry, infinite-dimensional symmetry groups, and quantum effects at null infinity.

Findings

Enlargement of the Poincaré group at null infinity

Geometric expressions for gravitational energy and momentum

Emergence of non-trivial vacuum configurations

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 K\"ahler 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 Poincar\'e 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.