Numerical Solutions of ideal two-fluid equations very closed to the event horizon of Schwarzschild black hole

摘要

The 3+1 formalism of Thorne, Price and Macdonald has been used to derive thelinear two-fluid equations describing transverse and longitudinal wavespropagating in the two-fluid ideal collisionless plasmas surrounding aSchwarzschild black hole. The plasma is assumed to be falling in radialdirection toward the event horizon. The relativistic two-fluid equations havebeen reformulate, in analogy with the special relativistic formulation asexplained in an earlier paper, to take account of relativistic effects due tothe event horizon. Here a WKB approximation is used to derive the localdispersion relation for these waves and solved numerically for the wave numberk.