Waves in general relativistic two-fluid plasma around a Schwarzschild black hole

Abstract

Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3 + 1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation. PACS: 95.30.Qd, 95.30.Sf, 97.60.Lf

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

“…The rate of damping or growth in that case is dependent on both frequency and radial distance from the horizon. These results are essentially agree with the results of SK [24] for ultrarelativistic limit and of Rahman [31] and Daniel and Tajima [23]for general relativity. For very low or negligible frequency, the plasmas are unstable, i.e., damped and growing modes exist as mansion above.…”

“…Since the majority of the modes show growth rates, the gravitational field is, in fact, feeding energy into the waves. This results are in accordance with the results of analytical studies carried out respectively by Mikhailovskii [33] and Rahman [31]. Figure 15: Left: Real part of a longitudinal complex mode for the electron-ion plasma.…”

“…The transverse part of the Maxwell's equations, Eqs. (31) and (32), and their resultant equation, Eq (33), are linearized to give…”

“…Recently, in Ref. [31] the two-fluid equations for transverse and longitudinal waves are simplified using action principle developed by Heintzmann and Novello [32] and solved using the analytical method developed by Mikhailovskii [33]. In this paper, the dispersion relations for transverse and longitudinal waves are solved numerically using WKB approximation.…”