Kerr-Schild Riemannian acoustic black holes in dynamo plasma laboratory

TL;DR

This paper investigates the presence and implications of acoustic black-hole metrics in dynamo plasma flows, showing their contribution to dynamo action and potential for modeling fast dynamos within a Kerr-Schild spacetime framework.

Contribution

It introduces a novel analysis of acoustic black-hole metrics in dynamo plasma flows, linking them to magnetic field growth and providing explicit Kerr-Schild spacetime models.

Findings

Acoustic black holes exist in dynamo plasma flows.

They contribute to the slow dynamo mechanism.

The effective metric can be expressed in Kerr-Schild form.

Abstract

Since Alfven, dynamo and sound waves and the existence of general relativistic black holes are well stablished in plasma physics, this provides enough motivation to investigate the presence of acoustic black-hole effective metric of analogue Einstein's gravity in dynamo flows. From nonlinear dynamo equations, one obtains a non-homogeneous wave equation where it is shown that the non-homogeneous factor is proportional to time evolution of the compressibility factor. In the Navier-Stokes case for a finite Reynolds number the acoustic black-holes also exists on the stretching plasma flows. In the magnetostatic case the dynamo is marginal. Analog models are usually applied to a superfluid analog spacetime, instead of the plasma setting used here. A coupled nonlinear plasma flow solution is found for the dynamo equation where the effective black hole solution of the scalar effective equation yields an imaginary part of the growth of magnetic field. Therefore though the real part of the growth rate of the magnetic field is negative or null, since there is a temporal oscillation in magnetic field, the solution represents a slow dynamo. Thus acoustic black holes are shown to definitely contribute to dynamo action of the effective plasma spacetime. It is suggested that a fast dynamo effective spacetime may also contain an acoustic black hole. I the case of planar waves the effective metric can be cast in Kerr-Schild spacetime form. The Killing symmetries are explicitly given in this metric and the growth of dynamo waves.