Relativistic Roche-Riemann problems around a black hole

Based on a framework of the hydrodynamics for a fluid star of mass m orbiting a Kerr black hole of mass M much greater than m, relativistic Roche-Riemann ellipsoids for incompressible fluids are considered. It is found that in the relativistic Roche-Riemann limit for the irrotational Roche-Riemann ellipsoid moving at the innermost stable circular orbit around Kerr black holes, the angular velocity, Omega, becomes Omega(2) similar or equal to 0.063637 pi rho. we also argue implications of present results on the final fate of black hole-neutron star binary systems.