Gravity from symmetry: Duality and impulsive waves

TL;DR

This paper shows that the dominant asymptotic Einstein equations at null infinity can be derived purely from the symmetry structure of the Weyl BMS (BMSW) group. By constructing covariant observables tied to Weyl scalars and introducing a duality in the gravitational phase space, the authors recast the evolution equations as conservation laws for a null fluid on I+, even in the presence of matter. They develop a non-radiative corner phase space with conserved charges and demonstrate non-linear impulsive gravitational waves that transition between vacua, encoding the full Weyl-scalar content non-perturbatively. The framework provides a path to quantize the asymptotic phase space via group representation theory and moment maps, linking memory, soft theorems, and corner symmetries. Overall, the work deepens the connection between asymptotic symmetries and gravitational dynamics, and lays groundwork for a holographic, symmetry-based quantum gravity program at null infinity.

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.