Gravitomagnetism and the significance of the curvature scalar invariants

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.

v2: Improved version conforming with prequel paper arXiv:2007.15384; new treatment of general Riemann tensor in Sec. III.C; new Sec. VI with non-vacuum examples; new appendix A; improved Sec. III.A; improved Secs. V.A and V.C, table II improved; added demonstration of equivalence between globally extrinsic gravitomagnetic curvature and field in vacuum; references added. v3: typo corrected

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Cited by in corpus (4)

• Curvature Invariants for accelerating Kerr-Newman black holes in (anti-)de Sitter spacetime
• Energy-momentum tensor and duality symmetry of linearized gravity in the Fierz formalism
• Spinning cylinders in general relativity: a canonical form for the Lewis metrics of the Weyl class
• Frame-dragging: meaning, myths, and misconceptions