  Waves propagating in the relativistic electron-positron or ions plasma are
investigated in a frame of two-fluid equations using the 3+1 formalism of
general relativity developed by Thorne, Price and Macdonald (TPM). The plasma
is assumed to be freefalling in the radial direction toward the event horizon
due to the strong gravitational field of a Schwarzschild black hole. The local
dispersion relations for transverse and longitudinal waves have been derived,
in analogy with the special relativistic formulation as explained in an earlier
paper, to take account of relativistic effects due to the event horizon using
WKB approximation
