Mathisson's helical motions demystified

The motion of spinning test particles in general relativity is described by Mathisson-Papapetrou-Dixon equations, which are undetermined up to a spin supplementary condition, the latter being today still an open question. The Mathisson-Pirani (MP) condition is known to lead to rather mysterious helical motions which have been deemed unphysical, and for this reason discarded. We show that these assessments are unfounded and originate from a subtle (but crucial) misconception. We discuss the kinematical explanation of the helical motions, and dynamically interpret them through the concept of hidden momentum, which has an electromagnetic analogue. We also show that, contrary to previous claims, the frequency of the helical motions coincides exactly with the zitterbewegung frequency of the Dirac equation for the electron.Comment: To appear in the Proceedings of the Spanish Relativity Meeting 2011 (ERE2011), "Towards new paradigms", Madrid 29 August - 2 September 201

Reference Frames and the Physical Gravito-Electromagnetic Analogy

The similarities between linearized gravity and electromagnetism are known since the early days of General Relativity. Using an exact approach based on tidal tensors, we show that such analogy holds only on very special conditions and depends crucially on the reference frame. This places restrictions on the validity of the "gravito-electromagnetic" equations commonly found in the literature.Comment: 9 Pages, 1 figure. To appear in the Proceedings of the IAU Symposium 261 "Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis", Virginia Beach, USA, 27 April - 1 May 200

Electromagnetic and Gravitational Invariants

The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects

Reference frames in General Relativity and the galactic rotation curves

The physical interpretation of the exact solutions of the Einstein field equations is, in general, a challenging task, part of the difficulties lying in the significance of the coordinate system. We discuss the extension of the International Astronomical Union (IAU) reference system to the exact theory. It is seen that such an extension, retaining some of its crucial properties, can be achieved in a special class of spacetimes, admitting non-shearing congruences of observers which, at infinity, have zero vorticity and acceleration. As applications, we consider the FLRW, Kerr and NUT spacetimes, the van Stockum rotating dust cylinder, spinning cosmic strings and, finally, we debunk the so-called Balasin-Grumiller (BG) model, and the claims that the galaxies' rotation curves can be explained through gravitomagnetic effects without the need for Dark Matter. The BG spacetime is shown to be completely inappropriate as a galactic model: its dust is actually static with respect to the asymptotic inertial frame, its gravitomagnetic effects arise from unphysical singularities along the axis (a pair of NUT rods, combined with a spinning cosmic string), and the rotation curves obtained are merely down to an invalid choice of reference frame -- the congruence of zero angular momentum observers, which are being dragged by the singularities.Comment: 29 pages, 10 figures. Slightly improved version, typos corrected, references added. Supplemental material is provided in the ancillary Mathematica files "NUTmetrics.nb" and "BGmetric.nb". Version to be submitte