Gravity from symmetry: Duality and impulsive waves

TL;DR

This paper derives asymptotic Einstein equations from symmetry principles involving the Weyl BMS group, revealing duality and impulsive gravitational waves as non-perturbative solutions, and offers a new perspective on quantizing gravitational vacua.

Contribution

It introduces a symmetry-based derivation of asymptotic Einstein equations including matter, identifying covariant observables and impulsive waves within the asymptotic phase space.

Findings

Identification of covariant conserved charges at null infinity

Recasting of asymptotic equations as conservation laws for a null fluid

Discovery of non-linear impulsive gravitational waves as vacuum transitions

Abstract

We show that we can derive the asymptotic Einstein's equations that arises at order $1/r$ in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provide a definition of conserved charges parametrizing the non-radiative corner phase space. These observables, related to the Weyl scalars, reveal a duality symmetry and a spin-2 generator which allow us to recast the asymptotic evolution equations in a simple and elegant form as conservation equations for a null fluid living at null infinity. Finally we identify non-linear gravitational impulse waves that describe transitions among gravitational vacua and are non-perturbative solutions of the asymptotic Einstein's equations. This provides a new picture of quantization of the asymptotic phase space, where gravitational vacua are representations of the asymptotic symmetry group and impulsive waves are encoded in their couplings.