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So all objects composed of matter emit black body radiation, which is photons of various frequencies. Is there an equivalent of black body radiation for other processes? Is there gluon black body radiation? Is there black body radiation in the form of gravitational waves?

In a related question, black holes can emit black body radiation due to their interaction with the electromagnetic field at the event horizon. Can this same kind of interaction happen with other fields, generating a similar type of radiation of other particles?

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Yes, all of the fields in quantum electrodynamics are excited in blackbody radiation, not just the electromagnetic field.

However, most of these fields are massive, so the minimum excitation energy is not accessible at ordinary temperatures. For instance, creation of a real electron-positron pair requires at least 1.022 MeV of mass-energy. If the temperature $kT \gg 1\,\rm MeV$, then the electron-positron field will come into thermal equilibrium with the electromagnetic field. But at lower temperatures, the massive particles find their antiparticles and annihilate, and there isn't enough energy in typical photon-photon interactions to replace them.

The matter blackbody fields are important in understanding Big Bang cosmology. One prediction is that there should be a cosmic neutrino background, with a slightly different temperature than the cosmic microwave background, because neutrinos decoupled from photons after the temperature became cold compared to the 1 GeV mass scale of the charged weak current.

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