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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?

Roger V.
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Zzyzx
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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.

Roger V.
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