  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, and 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
a bounded frequency range. 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.
