Two moment formalisms are developed for radiative transfer in a relativistic, differentially moving medium in flat or curved spacetime. One formalism applies to systems with no special symmetries; its moments of the photon direction distribution are ‘projected, symmetric trace-free tensors’ ℳα<inf>1</inf> α<inf>2</inf> …α<inf><it>k</it></inf>. The other formalism applies to systems with spherical, planar or pseudospherical symmetry; its moments are scalar functions analogous to the <it>J, H</it> and <it>K</it> of non-relativistic theory. Both formalisms come in three variants: a frequency-dependent variant (moments are functions of frequency <it>ν</it> and of location in spacetime <it>x</it>α); a redshifted variant applicable only to spacetimes with a ‘universal redshift function’ <it>R</it>(<it>x</it>α) (moments are functions of redshifted frequency <it>f</it> = <it>Rv</it> and of <it>x</it>α); and a frequency-integrated variant (moments are functions of <it>x</it>α only). The moment formalisms’ emission, absorption and scattering terms are evaluated explicitly for an unmagnetized, fully ionized medium whose electrons are non-degenerate and non-relativistic and are in thermal equilibrium with each other. It is shown that double Compton scattering (one photon in and two out) followed by Comptonization of the new photon (‘DC+C’)can be a far more effective source of photon energy than bremsstrahlung in hot, dilute plasmas [at <f>T/10⁷ \ K\>(\ρ₀/10⁻⁸\ g\⁻³)2/11</f>]. It is shown, further, that when the medium is sufficiently optically thick to Comptonization, DC + C can be described by a negative opacity (equation 6.43).
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K. S. Thorne (1981) studied this question.