Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations

Abstract

We identify in Einstein gravity an asymptotic spin-$2$ charge aspect whose conservation equation gives rise, after quantization, to the sub-subleading soft theorem. Our treatment reveals that this spin-$2$ charge generates a non-local spacetime symmetry represented at null infinity by pseudo-vector fields. Moreover, we demonstrate that the non-linear nature of Einstein's equations is reflected in the Ward identity through collinear corrections to the sub-subleading soft theorem. Our analysis also provides a unified treatment of the universal soft theorems as conservation equations for the spin-0,-1,-2 canonical generators, while highlighting the important role played by the dual mass.

36 pages; v2 minor revision

References in corpus (25)

• Asymptotic symmetries and subleading soft graviton theorem
• Evidence for a New Soft Graviton Theorem
• The gravitational-wave memory effect
• New symmetries for the Gravitational S-matrix
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• The Weyl BMS group and Einstein's equations
• Extended corner symmetry, charge bracket and Einstein's equations
• Sub-subleading soft gravitons and large diffeomorphisms
• Diagrammatic insights into next-to-soft corrections
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Isolated Surfaces and Symmetries of Gravity
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Next to subleading soft-graviton theorem in arbitrary dimensions
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• Shifting Spin on the Celestial Sphere
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• BMS Flux Algebra in Celestial Holography
• Gravity from symmetry: Duality and impulsive waves
• Celestial operator products from the worldsheet
• Coadjoint representation of the BMS group on celestial Riemann surfaces
• Hamiltonian derivation of dual gravitational charges
• Subsubleading soft graviton symmetry and MHV graviton scattering amplitudes
• Kinematical Gravitational Charge Algebra

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• Carrollian hydrodynamics from symmetries
• Goldilocks Modes and the Three Scattering Bases
• Metric reconstruction from celestial multipoles
• Charge and Antipodal Matching across Spatial Infinity
• Multipole expansion of gravitational waves: memory effects and Bondi aspects
• A Comment on Loop Corrections to the Celestial Stress Tensor
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Symmetries of the gravitational scattering in the absence of peeling
• Celestial Conformal Colliders
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Memory effects from holonomies
• Infrared finite scattering theory: Amplitudes and soft theorems
• Asymptotic Higher Spin Symmetries I: Covariant Wedge Algebra in Gravity
• $T\bar{T}$ deformed soft theorem
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• A Shorter Path to Celestial Currents
• Asymptotic Higher Spin Symmetries III: Noether Realization in Yang-Mills Theory
• On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Notes on self-dual gravity
• Asymptotic symmetries and soft theorems in higher-dimensional gravity
• Scalar subleading soft theorems from an infinite tower of charges
• Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory
• Double-soft limit and celestial shadow OPE from charge bracket