Anomalous magnetohydrodynamics in the extreme relativistic domain

TL;DR

This paper derives and analyzes the evolution equations of anomalous magnetohydrodynamics in the extreme relativistic regime, highlighting the effects of axial-vector currents and their suppression or disappearance under certain conditions.

Contribution

It introduces a relativistic formulation of anomalous MHD equations, including the effects of axial currents and their behavior in different physical regimes.

Findings

Anomalous contributions are suppressed by diffusivity.

In the perfect conductivity limit, anomalous effects vanish.

Explicit solutions are provided for irrotational, boost-invariant flows.

Abstract

The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost-invariant and with vanishing four-acceleration the corresponding evolution equations are explicitly integrated so that the various physical regimes can be directly verified.