How does frame dragging cause a stick to rotate in the opposite direction?

[Holesarecool]

Now, I've read that frame dragging will cause an effect likened to planetary gears, where the spinning source is the sun gear and the object is the planetary gear. Here's where I get confused.

Suppose you had a straight meter stick aimed directly at a massive rotating object from an equitorial radius > EH. If the rotation of the object is from left to right from your perspective, it seems that from my example, the part of the stick closer to the object will start to rotate towards the right, and the rear of the stick will rotate towards the left.

Now, since the material on the left hand side of the object is spinning 'towards' the stick, and the material on the right is moving away, shouldn't the affect of gravity be larger coming from the left hand side of the object? In the same sense that the light coming off of it will be at a higher wavelength on the left than the right due to GR.

I'm sure I've gone astray with an assumption here or there, but shouldn't this situation lead to a stick rotating in the opposite direction as predicted by frame dragging?

Thanks

 

[Jonathan Scott]

Now, I've read that frame dragging will cause an effect likened to planetary gears, where the spinning source is the sun gear and the object is the planetary gear. Here's where I get confused.

Suppose you had a straight meter stick aimed directly at a massive rotating object from an equitorial radius > EH. If the rotation of the object is from left to right from your perspective, it seems that from my example, the part of the stick closer to the object will start to rotate towards the right, and the rear of the stick will rotate towards the left.

Now, since the material on the left hand side of the object is spinning 'towards' the stick, and the material on the right is moving away, shouldn't the affect of gravity be larger coming from the left hand side of the object? In the same sense that the light coming off of it will be at a higher wavelength on the left than the right due to GR.

I'm sure I've gone astray with an assumption here or there, but shouldn't this situation lead to a stick rotating in the opposite direction as predicted by frame dragging?

Thanks

In GR the effective gravitational "force" is not due only to the scalar effect of the source mass (like an electrostatic field) but also has components due to the motion of the source material (like a magnetic field, only more complicated). Frame dragging is a direct effect of source motion.

Frame dragging (at least the rotational component) does not in itself cause motion locally; it is changes in frame dragging (with time or with changing position) which cause motion.

Rotational frame dragging is described by an angular velocity field. Locally, rotational frame dragging has the effect that something which is rotating at the rate which matches the frame dragging field feels as if it is not rotating and something which is at rest relative to the coordinate system experiences effects as if it were rotating the opposite way.