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

TL;DR

This paper derives and numerically solves the relativistic two-fluid wave equations near a Schwarzschild black hole's event horizon, revealing wave behaviors in accreting plasma.

Contribution

It reformulates the relativistic two-fluid equations in the black hole environment and applies a WKB approximation to analyze wave propagation.

Findings

Wave dispersion relations near the event horizon

Numerical solutions for wave number k

Insights into plasma wave behavior close to black holes

Abstract

The 3+1 formalism of Thorne, Price and Macdonald has been used to derive the linear two-fluid equations describing transverse and longitudinal waves propagating in the two-fluid ideal collisionless plasmas surrounding a Schwarzschild black hole. The plasma is assumed to be falling in radial direction toward the event horizon. The relativistic two-fluid equations have been reformulate, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here a WKB approximation is used to derive the local dispersion relation for these waves and solved numerically for the wave number k.