Image: WOLFGANG BRANDNER, EVA K. GREBEL (Universitat Wurzburg), et al., and the European Southern Observatory
By the time this matter has fallen past the point of no return, called the event horizon, it has concentrated the angular momentum of the black hole into a very small volume, which greatly distorts the surrounding space-time. The angular momentum persists even after the matter that caused it has cut itself off from our universe, collapsing beyond the event horizon.
Presently, a team of researchers at Stanford University is designing the Gravity Probe satellite to measure the distortion of space-time due to the angular momentum of our own spinning Earth. Although the space-time distortion near Earth is exceedingly weak compared to that around a black hole, the same physics are at work. Measuring this distortion would offer further support for Einstein's Theory of General Relativity.