Imagine we have a very tall vertical cylinder like a very elongated telegraph pole, that is rotating at 200 rpm about its long axis on near perfect bearings. Initially the cylinder is sufficiently far from a black hole, that differences in gravitational time dilation between the top and bottom of the cylinder are negligible for our purposes. Let us say there is observer that is stationary with respect to the black hole and located at the bottom of the cylinder. The cylinder is slowly lowered past this observer so that the top of cylinder becomes adjacent to this observer and lower part is very close to the black hole event horizon. Does anyone agree that the observer will see the part of the cylinder that is local to him, slow down significantly, (say by about 90%) and that it will speed back up to 200 rpm when the cylinder is raised again? Will an observer that accompanies the lower part of the cylinder always see that part rotate at approximately 200 rpm? If so, what does this say about conservation of angular momentum? P.S. Assume the cylinder is sufficiently rigid that it does not get twisted into knots by differences in speed between the top and bottom and that the lowering process is sufficiently slow for the rotation speeds to even out along the length of the cylinder.