On the (non) existence of a gravitomagnetic Dynamo

TL;DR

This paper investigates whether a gravitomagnetic dynamo can amplify intrinsic rotation, concluding that such amplification is impossible due to inconsistencies in the Galilean limit of gravitomagnetic equations.

Contribution

It demonstrates that a gravitomagnetic dynamo cannot exist within the Galilean limit of gravitomagnetic equations, clarifying the limitations of analogies with electromagnetic dynamos.

Findings

A gravitomagnetic dynamo cannot amplify intrinsic rotation.

The magnetic Galilean limit for gravitomagnetic equations is physically inconsistent.

The analogy with electromagnetic dynamo effects does not hold in this context.

Abstract

Due to the resemblance between Maxwell and the gravitomagnetic equations obtained in the weak field and slow motion limit of General Relativity, one can ask if it is possible to amplify a seed intrinsic rotation or spin motion by a gravitomagetic dynamo, in analogy with the well-known dynamo effect. Using the Galilean limits of the gravitomagnetic equations, the answer to this question is negative, due to the fact that a "magnetic" Galilean limit for the gravitomagnetic equations is physically inconsistent.