Diffeomorphism invariance and the black hole information paradox

TL;DR

The paper argues that diffeomorphism invariance reshapes the quantum gravity Hilbert space and observables, making boundary unitarity (BU) a robust feature when the Hamiltonian is a boundary term. It generalizes the information paradox to a Boundary Information Paradox (BIP) and proposes a resolution via nebulon-like boundary avatars that redundantly encode bulk information without violating the algebraic no-cloning theorem. The analysis leverages Wheeler-DeWitt dynamics and bulk reconstruction concepts while emphasizing nonperturbative gravitational effects that link boundary and bulk observables. The work reframes the infaller paradox as ill-posed in quantum gravity due to diffeomorphism-invariant observables and non-factorizable Hilbert spaces, offering a path to resolving paradoxes without invoking firewalls or breakdowns in local QFT. Overall, the paper highlights diffeomorphism invariance as the key to understanding information flow in quantum gravity and black hole contexts, with broad implications for low-energy effective theories and holographic embeddings.

Abstract

We argue that the resolution to the black hole information paradox lies in a proper accounting of the implications of diffeomorphism invariance for the Hilbert space and observables of quantum gravity. The setting of asymptotically Anti-de Sitter spacetime is adopted for most of the paper, but in the framework of canonical quantum gravity, without invoking AdS/CFT duality. We present Marolf's argument that boundary unitarity is a consequence of diffeomorphism invariance, and show that its failure to apply in the classical limit results from a lack of analyticity that has no quantum counterpart. We argue that boundary unitarity leads to a {\it boundary information paradox}, which generalizes the black hole information paradox and arises in virtually any scattering process. We propose a resolution that involves operators of the boundary algebra that redundantly encode information about physics in the bulk, and explain why such redundancy need not violate the algebraic no cloning theorem. We also argue that the infaller paradox, which has motivated the firewall hypothesis for black hole horizons, is ill-posed in quantum gravity, because it ignores essential aspects of the nature of the Hilbert space and observables in quantum gravity.