Effects of Schwarzschild Geometry on Isothermal Plasma Wave Dispersion

TL;DR

This paper investigates how Schwarzschild spacetime influences the dispersion and behavior of isothermal plasma waves near the horizon, using relativistic MHD equations and Fourier analysis.

Contribution

It formulates and analyzes the relativistic magnetohydrodynamical equations for isothermal plasmas in Schwarzschild spacetime, revealing wave characteristics near the horizon.

Findings

Complex dispersion relations derived for plasma waves.

Wave behavior varies near the Schwarzschild horizon.

Insights into wave propagation in curved spacetime environments.

Abstract

The behavior of isothermal plasma waves has been analyzed near the Schwarzschild horizon. We consider a non-rotating background with non-magnetized and magnetized plasmas. The general relativistic magnetohydrodynamical equations for the Schwarzschild planar analogue spacetime with an isothermal state of the plasma are formulated. The perturbed form of these equations is linearized and Fourier analyzed by introducing simple harmonic waves. The determinant of these equations in each case leads to a complex dispersion relation, which gives complex values of the wave number. This has been used to discuss the nature of the waves and their characteristics near the horizon.