Frame-dragging: meaning, myths, and misconceptions

TL;DR

This paper clarifies the concept of frame-dragging in general relativity, distinguishes its different levels and objects, debunks common misconceptions, and discusses various astrophysical applications.

Contribution

It provides a clear, nuanced analysis of frame-dragging effects, differentiating between three gravitomagnetic objects and correcting widespread misunderstandings.

Findings

Three levels of frame-dragging identified: potential, field, and tidal tensor.

Magnetic analogy is generally valid; fluid-dragging analogy is often misleading.

Common misconceptions like viscous body-dragging are debunked.

Abstract

Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ 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.