  The 3+1 formalism of Thorne and Macdonald has been used to derive the linear
two-fluid equations for transverse waves in the plasma closed to the
Schwarzschild-anti-de Sitter (SAdS) black hole. We reformulate the relativistic
two-fluid equations to take account of gravitational effects due to the event
horizon and negative cosmological constant and describe the set of simultaneous
linear equations for the perturbations. Using a local approximation we
investigate the one-dimensional radial propagation of Alfven and high frequency
electromagnetic waves. We derive the dispersion relation for these waves and
solve it for the wave number k numerically.
