Symmetries of the gravitational scattering in the absence of peeling

Abstract

The symmetries of the gravitational scattering are intimately tied to the symmetries which preserve asymptotic flatness at null infinity. In Penrose's definition of asymptotic flatness, a central role is played by the notion of asymptotic simplicity and the ensuing peeling behavior which dictates the decay rate of the Weyl tensor. However, there is now accumulating evidence that in a generic gravitational scattering the peeling property is broken, so that the spacetime is not asymptotically-flat in the usual sense. These obstructions to peeling can be traced back to the existence of universal radiative low frequency observables called "tails to the displacement memory". The universality of these tail modes is the statement of the classical logarithmic soft graviton theorem of Sahoo, Saha and Sen. Four-dimensional gravitation scattering therefore exhibits a rich infrared interplay between tail to the memory, loss of peeling, and universal logarithmic soft theorems. In this paper we study the solution space and the asymptotic symmetries for logarithmically-asymptotically-flat spacetimes. These are defined by a polyhomogeneous expansion of the Bondi metric which gives rise to a loss of peeling, and represent the classical arena which can accommodate a generic gravitational scattering containing tails to the memory. We show that while the codimension-two generalized BMS charges are sensitive to the loss of peeling at ${\mathcal{I}}^{+}$, the flux is insensitive to the fate of peeling. Due to the tail to the memory, the soft superrotation flux contains a logarithmic divergence whose coefficient is the quantity which is conserved in the scattering by virtue of the logarithmic soft theorem. In our analysis we also exhibit new logarithmic evolution equations and flux-balance laws, whose presence suggests the existence of an infinite tower of subleading logarithmic soft graviton theorems.

40 pages, published version, references added

References in corpus (32)

• Asymptotic symmetries and subleading soft graviton theorem
• Setting the boundary free in AdS/CFT
• New symmetries for the Gravitational S-matrix
• Radiative contribution to classical gravitational scattering at the third order in $G$
• The Weyl BMS group and Einstein's equations
• Generalized BMS charge algebra
• Sub-subleading soft gravitons and large diffeomorphisms
• Diagrammatic insights into next-to-soft corrections
• Computation of Displacement and Spin Gravitational Memory in Numerical Relativity
• Next to subleading soft-graviton theorem in arbitrary dimensions
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Loop-corrected subleading soft theorem and the celestial stress-tensor
• Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
• Conservation of asymptotic charges from past to future null infinity: Supermomentum in general relativity
• Multipole Expansion of Gravitational Waves: from Harmonic to Bondi coordinates
• The asymptotic structure of electromagnetism in higher spacetime dimensions
• Asymptotic structure of a massless scalar field and its dual two-form field at spatial infinity
• The Case Against Smooth Null Infinity I: Heuristics and Counter-Examples
• Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity
• Gravitational-wave tails of memory
• General null asymptotics and superrotation-compatible configuration spaces in $d\ge 4$
• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Multipole expansion of gravitational waves: memory effects and Bondi aspects
• Metric reconstruction from celestial multipoles
• Finite Charges from the Bulk Action
• Renormalization of conformal infinity as a stretched horizon
• On the Relation Between Asymptotic Charges, the Failure of Peeling and Late-time Tails
• Frequency space derivation of linear and non-linear memory gravitational wave signals from eccentric binary orbits
• The Case Against Smooth Null Infinity III: Early-Time Asymptotics for Higher $\ell$-Modes of Linear Waves on a Schwarzschild Background
• BMS charges in polyhomogeneous spacetimes
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory

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• Finite actions and asymptotic charges at null infinity for any spin
• Entanglement Rényi entropies in celestial holography
• Bondi Mass, Memory Effect and Balance Law of Polyhomogeneous Spacetime
• Flat Holography & Holographic Renormalization: Scalar Field
• Using thermodynamics to learn gravitational wave physics
• Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics