Quantum evolution of the Hawking state for black holes

TL;DR

This paper presents a general, regular quantum state evolution framework for Schwarzschild black holes that extends beyond standard Hawking radiation derivations, incorporating slice choices and mode bases, with implications for black hole information and dual CFT descriptions.

Contribution

It introduces a time-dependent, regular quantum state description of black holes that goes beyond asymptotic approximations and can incorporate interactions and different asymptotics.

Findings

Provides a regular, horizon-crossing slice-based evolving state

Shows Hawking quanta are produced near the horizon scale

Extends analysis to anti de Sitter space and dual CFT context

Abstract

We give a general description of the evolving quantum state of a Schwarzschild black hole, in the quantum field theory approximation. Such a time-dependent description is based on introducing a choice of time slices. We in particular consider slices that smoothly cross the horizon, and introduction of "stationary" such slices simplifies the analysis. This analysis goes beyond standard derivations of Hawking radiation that focus on asymptotic excitations, and in particular gives an evolving state that is regular at the horizon, with no explicit transplanckian dependence, and that can in principle be generalized to incorporate interacting fields. It is also expected to be useful in connecting to information-theoretic investigation of black hole evolution. The description of the evolving state depends on the choice of slices as well as coordinates on the slices and mode bases; these choices give different "pictures" analogous to that of Schr\"odinger. Evolution does have a simpler appearance in an energy eigenbasis, but such a basis is also singular at the horizon; evolution of regular modes has a more complicated appearance, whose properties may be inferred by comparing with the energy eigenbasis. In a regular description, Hawking quanta are produced in a black hole atmosphere, at scales comparable to the horizon size. This approach is also argued to extend to more general asymptotics, such as that of anti de Sitter space. In the latter context, this analysis provides a description of the hamiltonian and evolution of a black hole that may be compared to the large-$N$ dynamics of the proposed dual CFT.