Symmetries of the gravitational scattering in the absence of peeling

TL;DR

The article develops a comprehensive framework for gravitational scattering in four dimensions when peeling fails by formulating logarithmically-asymptotically-flat (LAF) spacetimes with polyhomogeneous Bondi expansions.It analyzes the solution space, evolution equations, and Weyl scalars, showing that peeling breakdown is encoded in new logarithmic data $D_{ab}$ and $E^{n,m}_{ab}$, while the BMSW/gBMS asymptotic symmetries persist and act consistently on this space.The authors construct a covariant phase-space formalism, derive a renormalized symplectic structure, and compute charges and fluxes; they find linearly divergent fluxes can be managed by matching, while logarithmic divergences from tails to memory reproduce and justify the classical logarithmic soft graviton theorem within the non-peeling regime.These results reinforce the link between asymptotic symmetries and soft theorems beyond the peeling paradigm and open avenues for exploring a hierarchy of subleading logarithmic memory and soft theorems in generic gravitational scattering.

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.