Effective black holes from non-Riemannian vortex acoustics in ABC flows

TL;DR

This paper investigates the formation of acoustic black-hole metrics in plasma dynamo flows, showing their contribution to dynamo action and potential for modeling fast dynamos within an effective spacetime framework.

Contribution

It introduces a novel connection between acoustic black holes and plasma dynamo flows, extending analogue gravity models to plasma physics and dynamo theory.

Findings

Acoustic black holes exist in plasma flows with finite Reynolds numbers.

They contribute to the slow dynamo mechanism through oscillatory magnetic field growth.

The effective metric in planar waves 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.