"According to the Kerr metric, such rotating black-holes should exhibit frame dragging, an unusual prediction of general relativity. Measurement of this frame dragging effect was a major goal of the Gravity Probe B experiment. Roughly speaking, this effect predicts that objects coming close to a rotating mass will be entrained to participate in its rotation, not because of any applied force or torque that can be felt, but rather because of the curvature of spacetime associated with rotating bodies. At close enough distances, all objects — even light itself — must rotate with the black-hole; the region where this holds is called the ergosphere."
Thanks bobby, my next question is since black holes seem to exhibit this effect, do relatively smaller objects cause this type of frame dragging as well, or do we consider the effects to be negligible given their incredibly smaller masses.
If you look up "Gravity Probe B" you will learn that this satellite did find a miniscule (really small) frame-dragging effect of the rotating earth. So, yes, the same applies to all rotating masses, but it is extremely small and hard or impossible to measure.