  In astronomy, the problem of black holes is arguably second in importance
only to the problem of cosmology. A current frontier in black hole research is
the measurement of spin. During the past three years, the spins of several
stellar-mass black holes in X-ray binaries have been measured via two
techniques: fitting the X-ray continuum spectrum and modeling the profile of
the Fe K line. This fledgling enterprise motivates the following decadal goals:
(1) Firmly establish the continuum-fitting and Fe K methods; obtain precise
values of spin for 10-20 black holes, several using both methods; (2) use the
derived masses and spins to test models of jets, GRBs, supernovae, black hole
formation, black hole binary evolution, etc.; (3) serve the IXO mission by
securing the Fe K methodology, which is currently the only means to measure the
spins of supermassive black holes in AGN; (4) identify the correct model of
high-frequency QPOs, thereby opening a third channel for measuring spin; (5)
pursue X-ray polarimetry as a means of securing the continuum-fitting and Fe K
methods, and also as a possible fourth avenue to spin; and (6) develop and test
MHD models of thin disks in strong gravity. Achieving these goals requires the
establishment of an RXTE follow-on mission dedicated to the study of bright and
transient compact objects, as well as strong support for theoretical work on 3D
MHD simulations of accretion flows in the Kerr metric of a spinning black hole.
