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Along the idea of frame-dragging;

Will the rotation of a black hole, which has some velocity v and angular momentum, influence its path in 3D space?

I've seen the fact that depending on the direction of the rotational velocity, the Kerr metric can give different revolution periods for orbiting masses. (e.g. as in our solar system)

So why (or why not) is this so?

How does the metric show that the direction of the velocity can influence orbital periods?

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I'm not understanding the last sentence. It seems to be asking how it can be, once you make the black hole spin, that objects orbiting the black hole care about the spin. But it's not clear how this relates to the rest of the question, which I'm interpreting as "will a spinning black hole necessarily follow the same path through empty space as a nonspinning one, if both start with the same velocity?" –  Chris White Feb 16 '13 at 17:49
    
I phrased the question clumsily, but your understanding of the question is correct. Will a spinning black hole follow the same path through empty space as a non spinning one? –  Zchpyvr Feb 16 '13 at 18:04

1 Answer 1

If the velocity $v$ is constant, and moving through a flat vaccuum, then the equivalence principle says that, in the co-moving frame of the black hole, all the orbits should be just like a black hole at rest. If you are measuring them with respect to a distant observer, then the observed periods should have a time dilation given by the standard $dt' = \gamma dt$

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So it has little do with frame-dragging then? –  Zchpyvr Oct 18 '12 at 19:17

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