The Relativistic Boltzmann Equation and the Equations of Magnetohydrodynamics with Radiative Reaction

Abstract

The relativistic collisionless Boltzmann equation with radiative reaction is derived from the conservation of the number of particles in the reduced six-dimensional phase space. It is then written in a covariant form. By taking invariant moments of the Boltzmann equation, we obtain the system of equations for relativistic magnetohydrodynamics taking account of radiative reaction. 21 and others have demonstrated that, for ultrarelativistic par­ ticles, the radiative reaction force can, in fact, be much greater than the Lorentz force. We have also shown explicitly that radiative reaction, although negligible at low temperatures, becomes dominant in the region of extremely high effective temperatures in our studies of relativistic plasma oscillations. 31 This suggests the necessity of including the force of radiative reaction in many astrophysical problems when the effective temperatures are extremely high. In the present work, we shall derive the relativistic Boltzmann equation and the equations of magnetohydro­ dynamics with radiative reaction taken into account. The formulation used here is similar to that of Goto, 41 and that of our previous work on relativistic classical scalar :fluid. 51 61