Deconstructing Frame-Dragging

Abstract

The vorticity of world-lines of observers associated with the rotation of a massive body was reported by Lense and Thirring more than a century ago. In their example, the frame-dragging effect induced by the vorticity is directly (explicitly) related to the rotation of the source. However, in many other cases, it is not so, and the origin of vorticity remains obscure and difficult to identify. Accordingly, in order to unravel this issue, and looking for the ultimate origin of vorticity associated to frame-dragging, we analyze in this manuscript very different scenarios where the frame-dragging effect is present. Specifically, we consider general vacuum stationary spacetimes, general electro-vacuum spacetimes, radiating electro-vacuum spacetimes, and Bondi–Sachs radiating spacetimes. We identify the physical quantities present in all these cases, which determine the vorticity and may legitimately be considered as responsible for the frame-dragging. Doing so, we provide a comprehensive, physical picture of frame-dragging. Some observational consequences of our results are discussed.

A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that

“…Costa et al [65] showed that the gravitomagnetic features can be used to distinguish (in the Weyl class of solutions describing the gravitational field of infinite cylinders) between the case of a static solution (the socalled Levi-Civita solution) and the one accounting for a rotating cylinder: in particular, in the latter case, a gravitomagnetic vector potential that cannot be eliminated by a global coordinate transformation is present. Herrera et al [66], Herrera [67] analysed the vorticity of the congruence of the observers world lines which, as we have seen above, is responsible for the dragging of inertial frames; their findings show that vorticity is related to the presence of a circular flow of super energy in the plane orthogonal to the vorticity vector, and this happens in stationary vacuum spacetimes and also in general Bondi-Sachs radiative ones.…”

On the Counter-Rotation of Closed Time-like Curves

“…One can say the same here for particles that are sufficiently close to the horizon of a Kerr-Taub-NUT black hole, but the interpretation ultimately does not work far away from the black hole. A very recent paper by Herrera has analyzed the physical cause of frame dragging in a variety of spacetimes; they are highly nontrivial [24].…”