FactChecker said:
Suppose we have the extreme case of a very massive, spinning black hole. Near the hole, the mathematics is dominated by the hole and even the rest of the entire universe becomes secondary. So the mathematics would start to look in the limit as though the black hole is stationary and the local space-time would correspond to that. Farther from the black hole, the mathematics returns to normal with the universe being stationary and the black hole spinning. The overall effect would be frame-dragging near the black hole.
I would welcome an expert opinion on the validity of this, admittedly crude, thought.
I'm not sure how well this will actually translate into the actual math.
It is true that, the closer you get to a spinning hole, the more the range of possible angular velocities (relative to infinity) you can have is constrained. The static limit, where the ergosphere starts, is where the constraint on possible angular velocities starts to exclude zero angular velocity--i.e., it's no longer possible, inside that limit, to
not have some positive angular velocity; the smallest angular velocity you can have becomes greater than zero. But there is also a constraint on the
largest angular velocity you can have, and the range between the two constraints gets tighter and tighter, until in the limit, as you approach the hole's horizon, the constraint tightens to a single possible angular velocity, the angular velocity of the hole itself.
I'm not sure that "the mathematics is dominated by the hole" is a good way to describe the above, though. The possible
kinematics (i.e., possible orbital parameters) are increasingly dominated by the "kinematics of the hole" in the sense described above. However, this is
not the same thing as frame dragging--although it has the same ultimate source, the spin of the hole. Frame dragging--the thing Gravity Probe B was testing for, Lense-Thirring precession--is an effect involving the direction in which spatial vectors fixed to a rigid body point as it orbits; it is
not an effect involving the parameters of the orbit itself (such as the possible angular velocities).