Schr\"odinger evolution of two-dimensional black holes

TL;DR

This paper analyzes the quantum evolution of two-dimensional black holes using Schr"odinger picture, revealing the entanglement structure, Hawking radiation, and potential pathways to unitarize black hole evolution.

Contribution

It introduces a Schr"odinger picture approach to study the dynamic quantum state of black holes, including matter evolution and entanglement, with implications for quantum gravity corrections.

Findings

Describes the evolving quantum state with different slicing choices.

Reveals the entanglement between Hawking quanta and interior partners.

Connects the evolution to potential quantum gravity corrections.

Abstract

This paper systematically treats the evolving quantum state for two-dimensional black holes, with particular focus on the CGHS model, but also elucidating features generalizing to higher dimensions. This is done in Schr\"odinger picture(s), to exhibit the dynamic evolution of the state at intermediate times. After a review of classical solutions, also connecting to descriptions of higher-dimensional black holes, it overviews the canonical quantum treatment of the full evolution, including gravitational dynamics. Derived in an approximation to this, following conversion to "perturbation picture," is the evolution of the quantum matter on the background geometry. Features of the evolving matter state are described, based on choice of a time slicing to put the evolution into ADM form. The choices of slicing as well as coordinates on the slices result in different quantum "pictures" for treating the evolution. If such a description is based on smooth trans-horizon slices, that avoids explicit reference to ultra-planckian modes familiar from traditional treatments, and exhibits the Hawking excitations as emerging from a "quantum atmosphere" with thickness comparable to the inverse temperature. Detailed study of the state exhibits the entanglement structure between Hawking quanta and the partner excitations inside the black hole, and the corresponding "missing information." This explicit description also allows direct study of the evolution and features, e.g. as seen by infalling observers, of these partner excitations, helping to address various puzzles with them. Explicit treatment of the evolving state, and its extension to higher dimensions, provides further connections to information theory and a starting point for study of corrections that can unitarize evolution, arising from new quantum gravity effects -- whether wormholes or something entirely different.