  We investigate transverse electromagnetic waves propagating in a plasma
influenced by the gravitational field of the Schwarzschild-de Sitter black
hole. Applying 3+1 spacetime split we derive the relativistic two-fluid
equations to take account of gravitational effects due to the event horizon and
describe the set of simultaneous linear equations for the perturbations. We use
a local approximation to investigate the one-dimensional radial propagation of
Alfv\'en and high frequency electromagnetic waves. We derive the dispersion
relation for these waves and solve it for the wave number $k$ numerically.
