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The evolution equations of anomalous magnetohydrodynamics are derived in theextreme relativistic regime and contrasted with the treatment of hydromagneticnonlinearities pioneered by Lichnerowicz in the absence of anomalous currents.In particular we explore the situation where the conventional vector currentsare complemented by the axial-vector currents arising either from the pseudoNambu-Goldstone bosons of a spontaneously broken symmetry or because of finitefermionic density effects. After expanding the generally covariant equations ininverse powers of the conductivity, the relativistic analog of the magneticdiffusivity equation is derived in the presence of vortical and magneticcurrents. While the anomalous contributions are generally suppressed by thediffusivity, they are shown to disappear in the perfectly conducting limit.When the flow is irrotational, boost-invariant and with vanishingfour-acceleration the corresponding evolution equations are explicitlyintegrated so that the various physical regimes can be directly verified.

Anomalous magnetohydrodynamics in the extreme relativistic domain