Frame dragging is a consequence of general relativity.

But don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if the spoon doesn't touch them. But I'm not satisfied with such simplistic explanations.

So if I understood it right rotating object cause a force that push nearby objects in the direction of rotation. Is that right, or something else happens? 

Is this a real force? So if I'm in the vicinity of a massive rotating object would I measure acceleration as I dragged around?

Does this effect caused by the mere fact of the rotation or does it caused by the gravitational anomalies? I mean that most rotating objects are not perfectly homogeneous rotating spheres. 

Can the stress energy tensor deal with rotation? I seems it can encode energy density, linear momentum, pressure and shear stress but doesn't seem to be encode angular momentum, can it?