What causes frame-dragging?

1. Apr 14, 2015

Warp

My question is simple, although I suspect the answer may not be: What exactly causes frame-dragging?

I'm not very adept at understanding GR equations, so you'll have to explain it in vernacular.

I find the concept of frame-dragging very interesting. One could posit the question: "If a black hole is rotating, how would you know which way it's doing so?" A very naive understanding of black holes would answer that you don't. However, the correct answer is that you measure frame-dragging in the vicinity of the event horizon (which can theoretically be done simply by dropping an object towards the black hole and seeing which direction it starts to move as it falls.)

(Another naive question would be "how can a point rotate? It has no dimensions, and thus can't possibly rotate." But the correct answer is that the singularity of a rotating black hole is not a point, but a ring, which is what "allows" it to rotate, so to speak.)

The concept of the ergosphere, which is caused by frame-dragging, is even more interesting. It baffles the mind that distances within the ergosphere may increase faster than c from the point of view of an external observer... which just raises so many questions.

2. Apr 14, 2015

rootone

I sure can't attempt a mathematical explanation, but I'm sure there are people here who can.
I'll place a dollar on gravity in the GR sense, and angular momentum in the Newtonian sense, being involved somewhere.

3. Apr 15, 2015

Ben Niehoff

Your naive questions come from a very basic misunderstanding of relativity, which I see turns up in this forum a lot. In fact, Einstein regretted calling his theory a theory of "relativity" because of exactly these kinds of confusions; he wished he had named it the "theory of invariances" instead, because it is really a theory about what is invariant when you change frames from one observer to another.

The fundamental misunderstanding I am talking about is the notion that "everything is relative". However, this is not true. Only velocity is relative. No observer can measure his own velocity in empty space, because velocity is only defined relative to other objects.

Acceleration, however, is not relative. An observer can measure his own acceleration with an accelerometer (a very simple device; you can attach a weight to a spring, for example). What an observer measures with an accelerometer is called that observer's "proper acceleration", and this includes the observer's rotation, which is a kind of acceleration. So rotation in empty space is real; it can be measured.

Your question of "Can a point rotate?" is more subtle than you may think, because an (idealized) observer is not just a point. An observer is a point with a local frame attached (a frame is a set of 4 orthogonal vectors, aligned along some choice of X, Y, Z, and T axes, which effectively function as the observer's set of measuring rods and clock). This frame can be made to rotate, and this is measurable.

P.S. The notion that "everything is relative" including acceleration is what is known as "Mach's principle". Einstein initially toyed with this idea, but in the end it turns out that GR is not Machian.

4. Apr 15, 2015

Staff: Mentor

Why do you think this?