Gravitational splitting at first order: Quantum information localization in gravity

TL;DR

This paper investigates how quantum information can be localized in gravity at leading order, proposing a gravitational splitting of the Hilbert space that aligns with gauge invariance and challenges soft hair solutions for black hole information.

Contribution

It introduces a leading-order gravitational splitting of the Hilbert space, providing a new framework for understanding quantum information localization in gravity.

Findings

Quantum information can be classically localized in a region with insensitivity to external measurements.

A gravitational splitting of the Hilbert space is defined at leading order in the gravitational coupling.

Soft hair does not resolve the black hole information paradox according to this framework.

Abstract

We explore the important fundamental question of how quantum information is localized in quantum gravity, in a perturbative approach. Familiar descriptions of localization of information, such as via tensor factorization of the Hilbert space or a net of commuting subalgebras of operators, conflict with basic gravitational properties -- specifically gauge invariance -- already at leading order in perturbation theory. However, previous work found that information can be classically localized in a region in a way such that measurements, including those of the gravitational field, outside the region are insensitive to that information, and only measure total Poincare charges. This paper shows that, working to leading order in the gravitational coupling, a similar quantum result holds, leading to a definition of a "gravitational splitting" on the Hilbert space for gravity. Such localization of information also argues against a role for "soft hair" in resolving the information problem for black holes. This basic mathematical structure plausibly plays a foundational role in the quantum description of gravity.