NUMERICAL SOLUTIONS OF IDEAL TWO-FLUID TRANSVERSE EQUATIONS VERY CLOSED TO THE EVENT HORIZON OF SCHWARZSCHILD–ANTI-DE SITTER BLACK HOLE

Abstract

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 Alfvén and high frequency electromagnetic waves. We derive the dispersion relation for these waves and solve it for the wave number k numerically.