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

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.