Gravity from symmetry: duality and impulsive waves

• Published in: The journal of high energy physics Vol. 2022; no. 4; pp. 125 - 58
• Main Authors: Freidel, Laurent, Pranzetti, Daniele
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 21.04.2022; Springer Nature B.V; SpringerOpen
• Subjects: Asymptotic properties; Classical and Quantum Gravitation; Classical Theories of Gravity; Conformal mapping; Conservation equations; Couplings; Elementary Particles; High energy physics; Isomorphism; Mathematical analysis; Models of Quantum Gravity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scalars; Space-Time Symmetries; String Theory; Symmetry; Tensors; Classical Theories of Gravity; Models of Quantum Gravity; Space-Time Symmetries
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP04(2022)125

A bstract 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.