There is a supermassive black hole in the center of the Milky Way. However, astronomers do not know if it is spinning or not. This article proposes a way that could be used to measure the spin over a relatively short amount of time through observing motions of stars that might be close enough to the black hole to show effects of relativity. The results of this article could be used in the future to guide such a search for these stars.
http://www.raa-journal.org/raa/index.php/raa/article/view/1801