On the (Non) Existence of a Gravitomagnetic Dynamo

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.

Gravitomagnetic field of a rotating superconductor and of a rotating superfluid

“…where m is the bare atomic mass in 4 He or twice the atomic mass of 3 He (due to Cooper pairing of atoms). Unfortunately, London's argument of n=0 in a closed loop does not hold in this case since the gravitomagnetic Meissner effect does not exist [16]. For a typical superfluid we will therefore find no contour in which the superfluid current will be zero (also the closed loop integration is not so simple due to the phenomena associated with vortices).…”

Gravitomagnetism and Gravitational Waves

“…Tartaglia and Ruggiero [57] investigated the possible occurrence of a GM analog of the Meissner effect using the same approximation for GTR. The non-existence of such a phenomenon in gravitation and of other putative GM effects has been demonstrated by Pascual-Sánchez [58].…”

“…For seeming analogies between Maxwellian electromagnetism and the fully non-linear equations of GTR, see the works by Matte [54] and, more recently, by Costa and Herdeiro [55]. In this framework, Pascual-Sánchez [56] discussed the non-existence of a GM dynamo in the linearized, weak-field and slow-motion approximation of GTR. Tartaglia and Ruggiero [57] investigated the possible occurrence of a GM analog of the Meissner effect using the same approximation for GTR.…”

Gravitomagnetic time-varying effects on the motion of a test particle

“…Actually, in General Relativity (GR) a GM field is indeed generated by the mass current: more in general, any theory that combines Newtonian gravity with Lorentz invariance must include a GM field. It is well known that the field equations of GR, in linear post-newtonian approximation, can be written in terms of Maxwell equations for the gravitoelectromagnetic (GEM) fields [2], [3] (for some limitations of this analogy see [4], while for a different approach to gravitoelectromagnetism based on the use of tidal tensors in GR, see [5,6]). In this context, the role of the gravitational induction has been recently investigated [7], and it has been shown that it is possible to describe gravitational induction in analogy with the Faraday-Lenz law of electromagnetism.…”