Hawking Radiation: A Comparison of Pure-state and Thermal Descriptions

TL;DR

This paper compares pure-state and thermal descriptions of Hawking radiation within a specific gravity model, revealing discrepancies at low energies and quantifying their differences, which are exponentially small at high energies.

Contribution

It provides a detailed comparison of pure and thermal state descriptions of Hawking radiation, including a quantitative measure of their difference in a dilaton gravity model.

Findings

Discrepancy in field-strength fluctuations at low energies

Coincidence of descriptions at high energies

Difference quantified and found exponentially small at high Hawking temperatures

Abstract

The cases of the Hawking radiation field being described by a pure state and by the usual thermal state are compared within the CGHS dilaton gravity model. The field-strength fluctuations of the Fourier modes are computed, showing a discrepancy in the low-energy regime, while coinciding at high energies. Then by defining a distance for density operators and evaluating it for the cases concerned, the difference between the pure and thermal descriptions is quantified and found to be exponentially small with respect to the Hawking temperature. Possible physical interpretations are discussed.