Abstract
The transverse electromagnetic waves propagating in a relativistic two-fluid plasma influenced by the gravitational field of the Reissner-Nordstr\"{o}m-de Sitter black hole has been investigated exploiting 3+1 split of spacetime. Reformulating the two-fluid equations, the set of simultaneous linear equations for the perturbations have been derived. Using a local approximation, the one-dimensional radial propagation of Alfv\'{e}n and high frequency electromagnetic waves are investigated. The dispersion relation for these waves is obtained and solved numerically for the wave number.
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