The Weyl BMS group and Einstein's equations

Abstract

We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes, besides super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein's equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.

53 pages + appendix, 1 figure; v3 minor revision to match published version

References in corpus (18)

• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Asymptotic symmetries and subleading soft graviton theorem
• Setting the boundary free in AdS/CFT
• Surface charge algebra in gauge theories and thermodynamic integrability
• New symmetries for the Gravitational S-matrix
• Extended corner symmetry, charge bracket and Einstein's equations
• Asymptotics and Hamiltonians in a First order formalism
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
• Asymptotic gravitational charges
• Hamiltonian derivation of dual gravitational charges
• Infinite towers of supertranslation and superrotation memories
• A note on dual gravitational charges
• Compact binary coalescences: The subtle issue of angular momentum
• Null infinity as an open Hamiltonian system
• Kinematical Gravitational Charge Algebra
• The Poisson bracket on free null initial data for gravity
• Sachs' free data in real connection variables

Cited by in corpus (80)

• Carrollian Perspective on Celestial Holography
• Extended corner symmetry, charge bracket and Einstein's equations
• Null boundary phase space: slicings, news and memory
• Embeddings and Integrable Charges for Extended Corner Symmetry
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Brown-York charges at null boundaries
• BMS Flux Algebra in Celestial Holography
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Loop-corrected subleading soft theorem and the celestial stress-tensor
• Gravity from symmetry: Duality and impulsive waves
• Edge modes as reference frames and boundary actions from post-selection
• Carrollian manifolds and null infinity: A view from Cartan geometry
• Holographic Lorentz and Carroll Frames
• The Precession Caused by Gravitational Waves
• Null Surface Thermodynamics
• Symmetries at Causal Boundaries in 2D and 3D Gravity
• Inferring fundamental spacetime symmetries with gravitational-wave memory: from LISA to the Einstein Telescope
• 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
• Brown-York charges with mixed boundary conditions
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• Non-Expanding horizons: Multipoles and the Symmetry Group
• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Wald-Zoupas prescription with (soft) anomalies
• Multipole expansion of gravitational waves: memory effects and Bondi aspects
• Metric reconstruction from celestial multipoles
• Ambiguity resolution for integrable gravitational charges
• Finite Charges from the Bulk Action
• Celestial Holography: Lectures on Asymptotic Symmetries
• Matrix Quantization of Gravitational Edge Modes
• Quantum Null Geometry and Gravity
• Symmetries of the gravitational scattering in the absence of peeling
• Renormalization of conformal infinity as a stretched horizon
• Null Infinity as a Weakly Isolated Horizon
• Horizons and Null Infinity: A Fugue in 4 voices
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Null Infinity and Horizons: A New Approach to Fluxes and Charges
• Gravitational memory effects and higher derivative actions
• Geometric relational framework for general-relativistic gauge field theories
• Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions
• Higher memory effects and the post-Newtonian calculation of their gravitational-wave signals
• Asymptotic Higher Spin Symmetries I: Covariant Wedge Algebra in Gravity
• Near horizon gravitational charges
• Dynamical symmetries of homogeneous minisuperspace models
• The dressing field method for diffeomorphisms: a relational framework
• Higher derivative asymptotic charges and internal Lorentz symmetries
• An Infrared On-Shell Action and its Implications for Soft Charge Fluctuations in Asymptotically Flat Spacetimes
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• BMS${}_3$ Mechanics and the Black Hole Interior
• Gyroscopic Gravitational Memory from quasi-circular binary systems
• Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group
• Conserved asymptotic charges for any massless particle
• Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space
• Asymptotic Limit of Null Hypersurfaces
• BRST BMS4 Symmetry and its Cocycles from Horizontality Conditions
• Null boundary gravitational charges from local Lorentz symmetries
• One-loop partition function of gravity with leaky boundary conditions
• On the covariant formulation of gauge theories with boundaries
• Asymptotic symmetries and memories of gauge theories in FLRW spacetimes
• Twisting asymptotic symmetries and algebraically special vacuum solutions
• Unveiling the electrodynamic nature of spacetime collisions
• Note on the group of vertical diffeomorphisms of a principal bundle, and its relation to the Frölicher-Nijenhuis bracket
• Null Surface Thermodynamics in Topologically Massive Gravity
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• Asymptotic dynamics and charges for FLRW spacetimes
• Entanglement Rényi entropies in celestial holography
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• On the Gravitational Precession Memory Effect for an Ensemble of Gyroscopes
• Null infinity as a Killing horizon
• Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory
• Using thermodynamics to learn gravitational wave physics
• Barnich-Troessaert Bracket as a Dirac Bracket on the Covariant Phase Space
• Asymptotic Structure with vanishing cosmological constant
• Mechanics as a general-relativistic gauge field theory, and Relational Quantization
• Superrotations are Linkages
• A Quasigroup Approach for Conservation Laws in Asymptotically Flat Spacetimes
• Shaving off soft hairs and the black hole image memory effect
• Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics