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# Surveys in Differential Geometry

## Volume 20 (2015)

### Geometry and physics of null infinity

Pages: 99 – 122

DOI: http://dx.doi.org/10.4310/SDG.2015.v20.n1.a5

#### Author

#### 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.

#### Keywords

Einstein equations, Cauchy problem, asymptotically flat spacetimes, stability, asymptotics, null infinity, ADM, gravitational radiation, memory effect, Christodoulou memory effect, classical theory, quantum theory, isolated gravitating system

#### 2010 Mathematics Subject Classification

35A01, 35L51, 35Q76, 83C05, 83C30, 83C35