Gravitomagnetism and the significance of the curvature scalar invariants

TL;DR

This paper clarifies the physical and algebraic meaning of curvature invariants in gravitation, explores their relation to gravitomagnetic effects, and proposes a new classification for intrinsic and extrinsic gravitomagnetism.

Contribution

It provides a detailed analysis of curvature invariants, their physical interpretation, and introduces a novel classification scheme for gravitomagnetism based on these invariants.

Findings

Curvature invariants determine observers measuring zero electric/magnetic fields.

Explicit velocities of such observers are derived in terms of measured fields.

A new classification scheme for intrinsic/extrinsic gravitomagnetism is proposed.

Abstract

The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a fundamental difference between the gravitomagnetic fields arising from the translational and rotational motions of the sources (which have been subject of observational and experimental tests, including the dedicated Gravity Probe-B and LARES space missions). In this work we clarify both the algebraic and physical meaning of the curvature invariants and their electromagnetic counterparts. They are seen to yield conditions for the existence of observers measuring vanishing electric/magnetic fields and gravitoelectric/gravitomagnetic tidal tensors, respectively. We determine these observers (in the gravitational sector and in the presence of sources, for the more relevant gravitomagnetic case) obtaining their velocities explicitly in terms of the fields/tidal tensors as measured by an arbitrary observer. The structure of the invariants of the astrophysical setups of interest is studied in detail, and its relationship with the gravitomagnetic effects is dissected. Finally, a new classification for intrinsic/extrinsic gravitomagnetism is proposed.