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In a semi-relativistic framework, which accounts for the mass of an energetic photon ($=h\nu/c^2$), a black body cannot emit a photon whose relativistic mass is greater than its own. So the higher the temperature and the lower the mass of the emitter, the more the high-energy side of the spectrum will deviate from Planck's formula, up to a hard cutoff at $\nu=m_{emitter}c^2/h$. Even below that energy, any emitted particle will still cause the emitter to recoil, Doppler-shifting the frequency of the emitted photon as seen by a stationary observer. When many photons are emitted, the combined recoils should result in something like Brownian motion of the emitter, with some kind of an effect on the spectrum.

How does one model this? Has this been modeled before? Obviously, there are implications for black hole evaporation. Will the mass/recoil effect slow down the rate of evaporation as the black hole gets smaller and hotter?

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    $\begingroup$ Are you talking about the "photon mass" in a medium as here ? opg.optica.org/ome/fulltext.cfm?uri=ome-11-8-2722 ? But the black body radiation is outside the body in the vacuum and there, there is no definition of a photon mass, it is zero. $\endgroup$
    – anna v
    Commented Jan 14, 2023 at 7:05
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Jan 14, 2023 at 10:03
  • $\begingroup$ I mean the relativistic mass of the photon (not the rest mass which is indeed zero). $\endgroup$
    – Zzyzx
    Commented Jan 14, 2023 at 15:57
  • $\begingroup$ I made a mistake in my question. I conflated classical black bodies and black holes. Classical black bodies (CBB) will only lose thermal energy through radiation. Black holes will lose rest mass. So, a classical CBB will not have an upper limit on how much it can radiate due to its rest mass; it still would be limited by its total thermal energy, which Planck's law doesn't account for: a body whose total thermal energy is 1 erg couldn't emit a 2 erg photon. $\endgroup$
    – Zzyzx
    Commented Jan 14, 2023 at 19:18

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Black body is mostly a historical concept, since black body radiation can be defined without recourse to a black body, see, e.g., this answer.

Also, if the body cannot emit photons beyond certain wavelength, it is also logical to question whether it can absorb photons of any wavelengths - i.e., whether it is really a black body:

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

If were to assume that we have an object that absorbs all the radiation, but can't emit certain wave lengths, then it would never come to thermodynamic equilibrium, although it might read a steady state where it absorbs as much high frequency radiation as it re-emits at lower wavelengths.

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