Observable Supertranslations

TL;DR

Addresses whether large-gauge, asymptotic symmetries in 4D gravity yield observable consequences. Replaces the formal soft variables with finite, observable memories $N$ and $C$ obtained via a sandwich construction around the hard radiative content, and derives the canonical bracket $\{N(\vartheta),C(\vartheta')\}=16\pi G\,\delta^2(\vartheta-\vartheta')$ from the Bondi news Dirac brackets. Demonstrates that the Strominger algebra and associated conservation laws emerge in an operational, observable framework and that soft and hard sectors decouple after a simple canonical transformation, preserving unitarity. Concludes that soft charges do not constrain hard scattering or resolve the black hole information problem, while providing a physically meaningful, observable realization of asymptotic memory physics.

Abstract

We show that large gauge transformations in asymptotically flat spacetime can be implemented by sandwiching a shell containing the ingoing hard particles between two finite-width shells of soft gauge excitations. Integration of the graviton Dirac bracket implies that our observable soft degrees of freedom obey the algebra imposed by Strominger on unobservable boundary degrees of freedom. Thus, we provide both a derivation and an observable realization of this algebra. The conservation laws associated with asymptotic symmetries are seen to arise physically from free propagation of infrared modes. This explains in physical terms our recent result that soft charges fail to constrain the hard scattering problem, and so cannot be relevant to the black hole information paradox.

Figures (2)

• Figure 1: Penrose diagram of a gravitational scattering process in asymptotically flat spacetime. The hard ingoing and outgoing particles are localized near $v=0$ and $u=0$ (left dashed wedge). Alice formally predicts an out-state on $\mathcal{I}^+$ from an in-state on $\mathcal{I}^-$ (top and bottom edges). Bob has only finite time, so he occupies a sphere of finite radius $r$ with freely falling equipment that produces the in-state and records the out-state. In $D=4$, Bob's sphere suffers deformations during the process.
• Figure 2: "Doubled" Penrose diagram: every point represents a hemisphere, which makes the antipodal relations visible. The interval ${\cal N}$ (yellow bands) is much greater than the duration of the hard flux (dashed cross). Its (conserved and observable) BMS charge $Q=Q_H+N$ generates observable BMS supertranslations on Bob's equipment. Here this is explicit as $N$ generates (conserved and observable) soft memories $C$ and $-C$ in the intervals $E$ and $L$, which deform Bob's sphere. $Q_H$ generates an angle-dependent time translation that completes this to a BMS transformation.