Solutions of Two Dimensional Viscous Accretion and Winds In Kerr Black Hole Geometry

We extend our previous studies of shock waves and shock-free solutions in thin accretion and winds in pseudo-Newtonian geometry to the case when the flow is ``two-dimensional'' and around a ``Kerr black hole''. We present equations for fully general relativistic viscous transonic flows and classify the parameter space according to whether or not shocks form in an inviscid flow. We discuss the behaviors of shear, angular momentum distribution, heating and cooling in viscous flows. We obtain a very significant result: we find that in weak viscosity limit the presence of the standing shock waves is more generic in the sense that flows away from the equatorial plane can produce shock waves in a wider range of parameter space. Similar conclusion also holds when the angular momentum of the black hole is increased. Generally, our conclusions regarding the shape of the shock waves are found to agree with results of the existing numerical simulations of the two dimensional accretion in Schwarzschild geometry. In a strong viscosity limit, the shocks may be located farther out or disappear completely as in the pseudo-Newtonian geometry.