Spinning Black Hole Drags Space-Time: What Causes Friction?

[happyhacker]

TL;DR Summary

Spinning Black Hole and it's connection with Space-time.

If a Black Hole is spinning (perhaps they all do) I have heard it distorts the 'fabric' of Space-time in the vicinity. What is the 'friction' component which allows the distortion?

 

[Ibix]

It's worth noting that we have actually looked for this frame dragging effect in the vicinity of the Earth with the Gravity Probe B satellite, and it's been detected as predicted (to available precision, anyway).

It isn't a frictional effect, though - spacetime isn't a fabric and doesn't have material properties like a coefficient of friction. Unfortunately, I'm not sure that there is an answer to your question. All that we know about spacetime is that it curves in the presence of matter and energy in a way described by the Einstein Field Equations. In the presence of spinning masses, the equations say that the curvature of spacetime is such that free-falling objects start to orbit in the direction of spin. Fundamentally, that means that we know what happens but we don't really have a deeper answer about mechanisms.

If we ever work out a quantum theory of gravity, then we may be able to provide some mechanism for the curvature effects that we predict and see. However, such a theory would have its own "just because" aspects - all physical theories do.

 

[FactChecker]

I would like to speculate as an amateur, if that is allowed in this forum, about something that might make frame-dragging more intuitive.
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.

 

[PeterDonis]

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).

 

[FactChecker]

@PeterDonis , Thanks. I appreciate your effort to explain it to a casual amateur. It is a tough subject. As long as my intuition is not completely absurd, I will probably just have to settle for it and not try to take it too literally. :-)