  We present a semi-analytic study of the equilibrium models of close binary
systems containing a fluid star (mass $m$ and radius $R_0$) and a Kerr black
hole (mass $M$) in circular orbit. We consider the limit $M\gg m$ where
spacetime is described by the Kerr metric. The tidally deformed star is
approximated by an ellipsoid, and satisfies the polytropic equation of state.
The models also include fluid motion in the stellar interior, allowing binary
models with nonsynchronized stellar spin (as expected for coalescing neutron
star-black hole binaries) to be constructed. Tidal disruption occurs at orbital
radius $r_{\rm tide}\sim R_0(M/m)^{1/3}$, but the dimensionless ratio $\hat
r_{\rm tide}=r_{\rm tide}/[R_0(M/m)^{1/3}]$ depends on the spin parameter of
the black hole as well as on the equation of state and the internal rotation of
the star. We find that the general relativistic tidal field disrupts the star
at a larger $\hat r_{\rm tide}$ than the Newtonian tide; the difference is
particularly prominent if the disruption occurs in the vicinity of the black
hole's horizon. In general, $\hat r_{\rm tide}$ is smaller for a (prograde
rotating) Kerr black hole than for a Schwarzschild black hole. We apply our
results to coalescing black hole-neutron star and black hole-white dwarf
binaries. The tidal disruption limit is important for characterizing the
expected gravitational wave signals and is relevant for determining the
energetics of gamma ray bursts which may result from such disruption.
