Frame-Dragging: Meaning, Myths, and Misconceptions

Abstract

Originally introduced in connection with general relativistic Coriolis forces, the term frame-dragging is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two analogies commonly employed, the analogy with magnetism holds strong where it applies, whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the first level) is, in general, misleading. Common misconceptions (such as viscous-type “body-dragging”) are debunked. Applications considered include rotating cylinders (Lewis–Weyl metrics), Kerr, Kerr–Newman and Kerr–dS spacetimes, black holes surrounded by disks/rings, and binary systems.

On the Rotation Curve of Disk Galaxies in General Relativity

“…(see, e.g., Landau &Lifshitz 1971 andPoisson &Will 2014, for a detailed description of higher-order post-Newtonian expansions; see also Rindler 1997;Lynden-Bell & Nouri-Zonoz 1998;Mashhoon et al 1999;Clark & Tucker 2000;Ruggiero & Tartaglia 2002;Mashhoon 2008;Costa &Natário 2021, andRuggiero 2021). We indicate with ∧ the vector (cross) product, ∇ is the usual nabla operator, and j = ρv is the gravitational current density, ρ and v being the mass density and velocity field of the sources.…”

All analytic solutions for geodesic motion in axially symmetric space-times

“…From the orbits of stars [1][2][3], and the imaging around supermassive black holes [4,5] through gravitational lensing [6], geodesic motions of particles and photons have a venerable history bringing results of General Relativity to observational grounds. Other important scenarios like frame dragging [7], radiation transport effects from accretion flows in the vicinity of relativistic stars [8], and gravitational waveform of merging compact objects [9], also require a detailed understanding of the geodesic motion in a general relativistic background.…”

A Note on the Gravitoelectromagnetic Analogy

“…In order to evaluate its impact, we need to compare it with the gravitomagnetic terms 2(β β β × B) i and 2 c ∂A i ∂t . As discussed, for instance, by Thorne and Hartle [29] and Costa and Natário [15],…”

“…However, we must always remember that GR is a non-linear theory, so the use of the linear gravitoelectromagnetic (GEM) analogy has some limitations, which need to be emphasised. To this end, it is useful to remember that it is also possible to develop an exact gravitoelectromagnetic analogy in full GR (see, e.g., Cattaneo [6], Costa and Herdeiro [7], Mashhoon et al [8] Ramos and Mashhoon [9], Costa and Natario [10], Chicone and Mashhoon [11], Rizzi and Ruggiero [12], Jantzen et al [13], Lynden-Bell and Nouri-Zonoz [14] and also the recent publication by Costa and Natário [15]). The purpose of this paper is to discuss, in full detail, the linear GEM analogy and its limitations.…”