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.
Highlights
The term “dragging” in the context of relativistic effects generated by the motion of matter was first coined by Einstein in his 1913 letter to Mach [1], in connection with the general relativistic Coriolis force generated in the interior of a spinning mass shell, causing the plane of a Foucault pendulum to be “dragged around”
It is the same for the precession of gyroscopes placed therein [4,5], in which case one talks about dragging of the “compass of inertia”
Very feeble in the solar system, where they have been subject of different experimental tests [89,90,91,92,93,94,95,96], gravitomagnetic effects become preponderant in the strong field regime, shaping the orbits of binary systems and the waveforms of the emitted gravitational radiation [101,102,103,104,105]
Summary
The term “dragging” in the context of relativistic effects generated by the motion of matter was first coined by Einstein in his 1913 letter to Mach [1], in connection with the general relativistic Coriolis force generated in the interior of a spinning mass shell, causing the plane of a Foucault pendulum to be “dragged around”. The underlying principle is the same as for the Coriolis forces that arise near a spinning body, in a reference frame fixed to the distant stars It is the same for the precession of gyroscopes placed therein [4,5], in which case one talks about dragging of the “compass of inertia” (the compass of inertia being defined as a system of axes undergoing Fermi–Walker transport, and physically realized precisely by the spin vectors of a set of guiding gyroscopes [6,7,8]). The basis vector corresponding to a coordinate φ is denoted by ∂φ ≡ ∂/∂φ, and its α-component by ∂αφ ≡ δφα
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