RELATIVISTIC PLASMAS NEAR A SCHWARZSCHILD BLACK-HOLE - A SOLUTION OF THE 2 FLUID ODES IN SCHWARZSCHILD COORDINATES

The 3+1 formalism of Thorne and Macdonald has been used to derive the linear two fluid equations describing the plasma surrounding a Schwarzschild black hole. These fluid equations lead to a set of ordinary differential equations for each of the transverse and longitudinal waves as well as for the two stream instability. The perturbations of density, velocity, and electromagnetic fields are obtained as functions of the radial coordinate r. Preliminary results are obtained for some simple cases by solving these sets of ODEs numerically as initial value problems with boundary conditions imposed at radial infinity. The results for the electric and magnetic field perturbations are rapidly oscillating functions of the radial coordinate where the rate of oscillation largely depends on the plasma and cyclotron frequencies which are also r dependent. From the results obtained for the perturbations the average electromagnetic energy densities are computed for the Alfvén, high frequency electromagnetic and longitudinal waves as well as the two stream instability. © 1995 The American Physical Society.