Thermality of the Hawking flux

Is the Hawking flux “thermal”? Unfortunately, the answer to this seemingly innocent question depends on a number of often unstated, but quite crucial, technical assumptions built into modern (mis-)interpretations of the word “thermal”. The original 1850’s notions of thermality — based on classical thermodynamic reasoning applied to idealized “black bodies” or “lamp black surfaces” — when supplemented by specific basic quantum ideas from the early 1900’s, immediately led to the notion of the black-body spectrum, (the Planck-shaped spectrum), but without any specific assumptions or conclusions regarding correlations between the quanta. Many (not all) modern authors (often implicitly and unintentionally) add an extra, quite unnecessary, assumption that there are no correlations in the black-body radiation; but such usage is profoundly ahistorical and dangerously misleading. Specifically, the Hawking flux from an evaporating black hole, (just like the radiation flux from a leaky furnace or a burning lump of coal), is only approximately Planck-shaped over an explicitly bounded range of frequencies. Standard physics (phase space and adiabaticity effects) explicitly bound the frequency range over which the Hawking flux is approximately Planck-shaped from both above and below — the Hawking flux is certainly not exactly Planckian, and there is no compelling physics reason to assume the Hawking photons are uncorrelated.