  A supermassive black hole can disrupt a star when its tidal field exceeds the
star's self-gravity, and can directly capture stars that cross its event
horizon. For black holes with mass M > 10^7 solar masses, tidal disruption of
main-sequence stars occurs close enough to the event horizon that a Newtonian
treatment of the tidal field is no longer valid. The fraction of stars that are
directly captured is also no longer negligible. We calculate generically
oriented stellar orbits in the Kerr metric, and evaluate the relativistic tidal
tensor at pericenter for those stars not directly captured by the black hole.
We combine this relativistic analysis with previous calculations of how these
orbits are populated to determine tidal-disruption rates for spinning black
holes. We find, consistent with previous results, that black-hole spin
increases the upper limit on the mass of a black hole capable of tidally
disrupting solar-like stars to ~7 x 10^8 solar masses. More quantitatively, we
find that direct stellar capture reduces tidal-disruption rates by a factor 2/3
(1/10) at M = 10^7 (10^8) solar masses. The strong dependence of
tidal-disruption rates on black-hole spin for M > 10^8 solar masses implies
that future surveys like LSST that discover thousands of tidal disruption
events can constrain supermassive black-hole spin demographics.
