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Massive spinning objects (such as Kerr black holes) 'twist' spacetime around them, as predicted by Einstein's theory of general relativity. Can someone explain qualitatively why this happens? Is there a fairly simple relation between the mass, radius, and angular velocity of the spinning object, and the degree of frame-dragging that occurs.

N.B.: I only have a basic understanding of Einstein's field equations and tensor calculus.

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You can get a qualitative feeling about this effect by looking at the Einstein field equations. $$R_{\mu \nu}-\frac{R}{2}g_{\mu \nu}=8 \pi GT_{\mu \nu}$$ The right hand side describes the curvature of spacetime and the left handside the energy momentum content. Now a rotating object has a different energy momentum tensor than a nonrotating object (There are extra terms due to angular momentum and rotational energy). Of course the spacetime curvature will react to these extra terms. This leads to the frame dragging you mentioned. However I think there is no simple general relation, which you wish for. There is a solution in a weak field approximation to this problem (Lense Thirring precession), but this of course does not apply to Kerr black holes.

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