Could a very small black hole where half of its entropy has been radiated, emit Hawking radiation that is macroscopically distinct from being thermal? i.e: not a black body radiator. Or would the scrambling property mean that the initial states that produce the non-thermal Hawking radiation are micro states that are macroscopically indistinguishable from micro states that lead to Hawking radiation that is nearly thermal?

For the sake of the question, if two microscopic states are macroscopically indistinguishable, it should be assumed that preparing the state in one or the other is physically impossible, even if it is possible in principle.

a reference to a recent TRF post about thermal and pure states of black holes being macroscopically indistinguishable from the outside

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    $\begingroup$ If you believe that Hawking radiation is not thermal, then it has to be massively entangled. You could distinguish it from thermal radiation only by looking at the entire history of the radiation output from the black hole. $\endgroup$ – Peter Shor Dec 26 '12 at 17:36
  • $\begingroup$ hi @PeterShor, the original question was if by an appropriate preparation, you could make the hawking radiation be, for example, coherent. I replaced the term 'coherent' to be 'distinguishably non-thermal' which because i thought it was too stringent to make meaningful considerations. But the point my question is about is if you could change the statistical properties of the Hawking radiation by appropiate preparation of the state (to be continued..) $\endgroup$ – lurscher Dec 26 '12 at 18:39
  • $\begingroup$ suppose for instance, i create a black hole by collapse of a electromagnetic spherically symmetric, convergent wavefront. Assume the wavefront is in a coherent, prepared state of the experimenter's choice $\endgroup$ – lurscher Dec 26 '12 at 18:40

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