Schrödinger evolution of two-dimensional black holes

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 Schrödinger 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.

41 pages, 5 figures

References in corpus (12)

• JT gravity as a matrix integral
• Black hole information, unitarity, and nonlocality
• Observables, gravitational dressing, and obstructions to locality and subsystems
• Unitarity and Holography in Gravitational Physics
• Possible observational windows for quantum effects from black holes
• How is quantum information localized in gravity?
• A global picture of quantum de Sitter space
• Holography from the Wheeler-DeWitt equation
• Quantization in black hole backgrounds
• Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim Gravity
• Black hole evaporation without an event horizon
• An exact derivation of the Hawking effect in canonical formulation

Cited by in corpus (6)

• UV And IR Effects On Hawking Radiation
• Quantum evolution of the Hawking state for black holes
• A "black hole theorem," and its implications
• Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
• TCC bounds on the static patch of de Sitter space
• General radially moving references frames in the black hole background