Group velocity and causality in standard relativistic resistive magnetohydrodynamics

TL;DR

This paper investigates whether superluminal group velocities in resistive relativistic MHD imply causality violations, finding through simulations that no acausal effects occur, thus supporting the consistent use of these equations.

Contribution

The study demonstrates through numerical simulations that superluminal group velocities in resistive RMHD do not lead to causality violations, confirming the equations' physical consistency.

Findings

Superluminal group velocities do not cause acausal phenomena.

Numerical simulations show no information traveling to the past.

Results align with linear wave train propagation theory.

Abstract

Group velocity of electromagnetic waves in plasmas derived by standard relativistic resistive MHD (resistive RMHD) equations is superluminal. If we assume that the group velocity represents the propagation velocity of a signal, we have to worry about the causality problem. That is, some acausal phenomena may be induced, such that information transportation to the absolute past and spontaneous decrease in the entropy. Here, we tried to find the acausal phenomena using standard resistive RMHD numerical simulations in the suggested situation of the acausal phenomena. The calculation results showed that even in such situations no acausal effect happens. The numerical result with respect to the velocity limit of the information transportation is consistent with a linear theory of wave train propagation. Our results assure that we can use these equations without problems of acausal phenomena.