Understanding Frame Dragging: Exploring the Effects of Black Hole Rotation

[tkav1980]

Im having some trouble wrapping my head around this concept. I don't have the math background i really need to fully understand it which i suppose is causing my confusion.

I picture a black hole. some distance outside of the Event horizion, i have a man floating in space. The black hole is rotating counter clockwise, and the man's left shoulder is facing the black hole at its equator. the mans right shoulder is stationary relative to some distant constellation. If this man extens both arms like a T, the way space is bending his left hand would be pulled in the direction of the spin of the black hole and his right hand would be pulled in the opposite direction.


I keep trying to figure this out but that picture i have in my head doesn't make any sense to me. I feel like I am missing some major principle, and Wikipedia has been of no help, hahaha.

Is there regions of space being pulled along with the rotation direction of the black hole, and another region farther away being tourqued in the opposite direction? Or is the right hand being pulled in the opposite direction because it isn't actually being pulled but remaining stationary relative to the far off constellation so it gives the illusion of doing so?

 

[WannabeNewton]

All particles within the ergosphere must rotate with the hole. If you initially send a photon in the same direction as the hole's rotation then it will rotate with the hole. If you send a photon that moves in the direction opposite the rotation then initially it won't be able to move at all. So all massive particles would have to rotate with the hole even if they have a significant angular momentum in the opposite direction and within the ergoregion photons and massive particles must rotate with an angular momentum that has the same sign as that of the black hole's. Even far away, there will be a frame dragging effect on massive particles with an angular momentum having the same sign as that of the hole but the effect falls off roughly as 1/r^3.

 

[Bill_K]

tkav, There are several effects associated with Kerr black holes. What WannabeNewton says about the "frame dragging" of the orbits is correct, but it's not what you're referring to. I think you got the "man with arms extended" example from Wikipedia, and unfortunately they give a really poor explanation of it.

The issue your man is dealing with is called the "locally nonrotating frame." In general relativity, rotation is absolute. An observer can tell unambiguously whether or not he is rotating. How can he tell? Answer: he carries a gyroscope, and the direction that the axis of the gyroscope points defines his local nonrotating frame. (Three gyroscopes at right angles to each other work even better.) The other way to determine nonrotation would be by looking at the distant stars. And normally the two methods agree, but near a Kerr black hole they do not! The stars and the gyroscope move with respect to each other.

Wikipedia is using an ice skater as the gyroscope. As she starts from rest and extends her arms, she defines a locally nonrotating frame. Note she is not experiencing a "torque" or anything like that. And it is not because one arm is closer to the hole. She's doing the best she can to remain nonrotating. If she wanted, she could certainly spin herself any other way, e.g. to remain facing the hole. But in that case she'd feel she was rotating. For example centrifugal force would cause blood to rush to her hands.

Everywhere near a Kerr black hole the local nonrotating frame does rotate with respect to the fixed stars.