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, as explained in an earlier paper, to take account of gravitational effects due to the event horizon. Here, a local approximation is used to investigate the one-dimensional radial propagation of longitundial waves. A study is also included of the two stream instability in view of its importance in astrophysics. Dispersion relations are obtained for these waves and solved numerically for the wave number k.

• Received 12 May 1994

DOI:https://doi.org/10.1103/PhysRevD.51.6677