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.
Highlights
Black holes appear to be the most mysterious objects in the cosmos, and a primary reason for this is the predicted phenomenon of Hawking evaporation [1] and the associated question of the fate of information that they capture.A useful way to study the information content of a black hole (BH) is through the entanglement of its quantum states with outside degrees of freedom
This paper systematically treats the evolving quantum state for twodimensional black holes, with particular focus on the CGHS model, and elucidating features generalizing to higher dimensions
A BH can build up this entanglement either by absorbing entangled matter, or it naturally builds up such entanglement via the Hawking process
Summary
Black holes appear to be the most mysterious objects in the cosmos, and a primary reason for this is the predicted phenomenon of Hawking evaporation [1] and the associated question of the fate of information that they capture. This is most naturally done by working in a Schrödinger picture, to describe the evolving quantum state. In a regular description, based on a smooth trans-horizon slicing, one can find the explicit form of the hamiltonian, and see both the smooth structure of the quantum atmosphere as well as the connection to the more singular energy eigenstate basis This leads to an explicit treatment of the Hawking evolution which supports many of the features which have been generally appreciated, but in a more complete description, which is readily generalized to the interacting case. Sections three and four can be skipped by those readers only interested in the description of evolution of the quantum state on a fixed BH geometry
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