Relativistic two fluid plasmas in the vicinity of a Schwarzschild black hole—Local approximation. I

Abstract

The 3+1 split of general relativity is used in a preliminary investigation of waves propagating in a plasma influenced by the gravitational field of a Schwarzschild black hole. The relativistic two fluid equations have been reformulated to take account of gravitational effects due to the event horizon. The set of simultaneous linear equations for the perturbations are displayed but the numerical solution in Schwarzschild coordinates is reserved for a subsequent paper. Here, a local approximation is used to investigate the one-dimensional radial propagation of Alfv\'en and high frequency electromagnetic waves. The dispersion relation is obtained for these waves and solved numerically for the wave number k.