Electromagnetic Properties of Stellar Matter. I. Dielectric Permeability of a Hot Rarefied Plasma with Abundant Production of Electron-Positron Pairs

The Vlasov equations are used to determine the transverse and longitudinal dielectric permeabilities of a hot, rarefied ultrarelativistic electron-positron plasma. The Fermi distribution is used as the unperturbed distribution function of the electrons and positrons. It is shown that, owing to the abundant production of electron-positron pairs, the plasma frequency of the ultrarelativistic plasma increases linearly with rising temperature. Here the ratio of the frequency at which the spectral density of the equilibrium emission is maximal to the plasma frequency remains fixed and equals 28. It is shown that in this sort of plasma, in particular in the matter of the early universe in the ultrarelativistic electronpositron epoch, the spectrum of the radiation differs very little from black-body radiation.