Seeing Page Curves and Islands with Blinders On

TL;DR

This paper argues that in quantum gravity, the algebra of observables is complete and non-factorizing, which challenges traditional views on the Page curve and black hole information loss, showing that information is encoded in asymptotic data.

Contribution

It demonstrates that the algebra of observables in quantum gravity is complete and non-factorizing, altering the understanding of information flow and the origin of the Page curve.

Findings

Black hole interior can be reconstructed from exterior data.

Page curves can be obtained by removing the Hamiltonian from the algebra.

Information is encoded in asymptotic observables, not emerging from the black hole.

Abstract

This paper summarizes recent discussions of the Page curve and the information paradox, and responds to the reasoning and examples from arXiv:2506.04311. We review arguments demonstrating that in quantum gravity the algebra of observables at infinity is complete, both in AdS and in asymptotically flat space. This completeness implies that the bulk Hilbert space in quantum gravity does not factorize along the radial direction, undermining a key common assumption in Hawking's argument for information loss and in initial derivations of the Page curve. As a consequence, in a standard theory of gravity, information does not ``emerge'' from a black hole in the manner suggested by the Page curve; rather, it is already encoded in asymptotic observables. Relatedly, the full black hole interior, and not just an ``island'', can be reconstructed from exterior data. Page curves and islands can be obtained by removing the Hamiltonian from the exterior algebra. This may be implemented operationally by restricting access to part of the asymptotic region (a detector with a ``blind spot'') or, in the special case of null infinity in asymptotically flat spacetimes, by formally discarding the Hamiltonian from the set of observables despite its physical accessibility. Such Page curves describe only the redistribution of information between measured and unmeasured degrees of freedom, rather than fundamental information recovery. Finally, Page curves and islands also arise when a black hole is coupled to a nongravitational bath, a setup that yields a nonstandard theory of gravity. We show how, even in this setting, the unusual localization of information in gravity provides a concrete physical mechanism for information transfer from the gravitational system into the bath.