Covariant kinetic theory with an application to the Coma cluster

In this paper, we introduce a novel solution to the covariant Landau equation for a pure electron plasma. The method conserves energy and particle number and reduces smoothly to the Rosenbluth potentials of nonrelativistic theory. We find that the covariant relaxation timescale agrees with past results; however, as a full solution to the covariant Boltzmann equation, our technique allows for anisotropic or degenerate distributions, which makes it unique. To demonstrate the power of our solution in dealing with hot, astrophysical plasmas, we use this technique to show that one of the currently considered models, continuous stochastic acceleration of thermal electrons, for the hard X-ray emission in the Coma Cluster actually cannot work because the energy gained by the particles is distributed to the whole plasma on a timescale much shorter than that of the acceleration process itself.