Longitudinal Wave Propagation in Relativistic Two-fluid Plasmas around Reissner-Nordstrom Black Hole

TL;DR

This paper investigates the behavior of longitudinal waves in a relativistic two-fluid plasma near a Reissner-Nordstrom black hole using the 3+1 formalism of general relativity, deriving and numerically solving the dispersion relation.

Contribution

It introduces a local approximation method to analyze longitudinal wave propagation in relativistic plasmas around charged black holes, deriving the dispersion relation.

Findings

Derived the dispersion relation for longitudinal waves in the plasma.

Numerically solved the dispersion relation for wave number k.

Analyzed the effects of the black hole's gravitational field on wave propagation.

Abstract

The 3+1 spacetime formulation of general relativity is used to investigate the transverse waves propagating in a plasma influenced by the gravitational field of Reissner-Nordstrom black hole, as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here, a local approximation is used to investigate the one-dimensional radial propagation of longitudinal waves. We derive the dispersion relation for these waves and solve it numerically for the wave number k.