The Holographic Nature of Null Infinity

TL;DR

The paper argues that in four-dimensional asymptotically flat quantum gravity, all information about massless excitations is holographically stored in an infinitesimal neighborhood near the past boundary of future null infinity, and that information on any cut of null infinity can be accessed from earlier cuts, reshaping the understanding of the black hole information paradox. It develops a canonical framework using Bondi data, soft/hard charges, and algebras near cuts, and proves, under reasonable assumptions, two key results about information storage and a nested structure across cuts. The findings imply that the fine-grained von Neumann entropy on segments of future null infinity is invariant with respect to retarded time, challenging the Page curve intuition in flat space and in AdS/CFT analogues. Overall, the work proposes a coherent flat-space holography program grounded in asymptotic symmetries and canonical gravity, with broad implications for information preservation and holographic encoding.

Abstract

We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space.

Figures (6)

• Figure 1: The main results of our paper are displayed in yellow ovals, with numbers in adjoining circles. The purple rectangles indicate physical assumptions. Dependence of a result on an assumption is indicated by a dashed line. Implications between results are denoted by thick black lines.
• Figure 2: The naive Page curve. If one incorrectly assumes that the Hilbert space factorizes into degrees of freedom outside and inside the black hole, the von Neumann entropy of the radiation that has emerged till retarded time $u$ on ${{\cal I}^{+}}$ is expected to obey the curve above indicating that "information is gradually returned to the exterior."
• Figure 3: The fine-grained von Neumann entropy (right) of any state of massless excitations reduced on a segment that extends till the cut at $u$ marked on the left figure. The result directly follows from the arguments above. The information is always outside, and so the entropy never goes up or comes down!
• Figure 4:
• Figure 5: In ordinary local quantum field theories we can specify some feature in the wavefunction inside a bounded region (depicted by the bump) without affecting the wavefunction outside. But, in gravity, not only is one forced to modify the wavefunction outside the region (shown by the wiggles), the constraints are so strong that the detailed wavefunction outside completely fixes it inside.

Theorems & Definitions (4)

• Definition 1
• Definition 2
• Definition 3
• Lemma 1