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I am trying to understand subject effect in the framework of general relativity. Wikipedia says as follows:

imagine that a north–south-oriented ice skater, in orbit over the equator of a rotating black hole and rotationally at rest with respect to the stars

Than, frame dragging is described as:

Also, an inner region is dragged more than an outer region.

This would suggest to me, with thinking of dragging as some kind "viscosity", that the BH would transfer some of its angular momentum to the orbiting body. But following text contradicts this:

This produces interesting locally rotating frames. For example, imagine that a north–south-oriented ice skater, in orbit over the equator of a rotating black hole and rotationally at rest with respect to the stars, extends her arms. The arm extended toward the black hole will be "torqued" spinward due to gravitomagnetic induction. Likewise the arm extended away from the black hole will be torqued anti-spinward. She will therefore be rotationally sped up, in a counter-rotating sense to the black hole. This is the opposite of what happens in everyday experience.

, indicating that orbiting body would receive angular momentum of opposite sign than angular momentum of the BH (thus enlarging the angular momentum of the BH, if angular conservation law is to be believed). So, my first question is - what is the orientation of the angular momentum this skater, initially unrotating w.r.t. far stars, would receive from the BH through the mechanism of frame dragging? Spinwise or counter-spinwise of angular momentum of BH?

Second, things get even weirder. It says:

There exists a particular rotation rate that, should she be initially rotating at that rate when she extends her arms, inertial effects and frame-dragging effects will balance and her rate of rotation will not change.

I read this as if, there is a frequency of rotation that would cancel influence of frame dragging. This is weird to me because I am thinking of frame dragging as a torque and it is claimed that somehow this torque balanced is with predefined frequency of rotation. With some momentum of inertia, torque is time derivative of the angular momentum and are independent degrees of freedom thus unclear how they cancel. Or does that mean that frame dragging spins up orbiting body to some limit frequency and saturates at it?

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  • $\begingroup$ I like to think of gravity like a low pressure system. So think of standing next to a tornado, and extending your arms. The arm nearest to the tornado would spin with the wind, and the other arm would spin in the opposite direction, assuming that you are pinned to the ground strongly enough. But in reality the tornado would just pull your whole body along with the wind. The same thing would happen with frame dragging unless you were very securely pinned in place. $\endgroup$
    – foolishmuse
    Commented May 1, 2023 at 23:00
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    $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented May 2, 2023 at 2:22
  • $\begingroup$ Imagine a water channel where water runs the opposite ways at the opposite sides and is still at the center. If you are at the center and extend your hands to the sides, then clearly there is a certain rotation speed, at which your hands move at the same speed as water, so the movement of water has no effect on your rotation. Now imagine the whole channel moves in one direction, so all water in it also moves in one direction, just at different speeds. Finally, the direction of the channel motion is around a black hole, but water still has no effect on your rotation. What do you think is weird? $\endgroup$
    – safesphere
    Commented May 2, 2023 at 5:02
  • $\begingroup$ @foolishmuse Exactly, my friend! Note that if you are rotating with the wind around the tornado, then your outer hand does not rotate in the opposite direction. To see this, imagine a marble rolling inside a pipe. While the marble itself may see its sides rotating in the opposite directions, you observe that all parts of the marble move only in the direction of rotation. Thus your comment correctly illustrates frame dragging. $\endgroup$
    – safesphere
    Commented May 2, 2023 at 5:17
  • $\begingroup$ @safesphere correct. I should not have said spin in the opposite direction because that implies rotation. I should have said move in the other direction. If one hand moves North the other moves South in the same rotation circle $\endgroup$
    – foolishmuse
    Commented May 2, 2023 at 13:13

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