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 in which the flow is two-dimensional and around a Kerr black hole. We present equations for fully general relativistic viscous transonic hows and classify the parameter space according to whether or not shocks form in an inviscid how. We discuss the behaviors of shear, angular momentum distribution, and heating and cooling in viscous hows. We obtain a very significant result: in the weak-viscosity limit, the presence of standing shock waves is more generic, in the sense that hows away from the equatorial plane can produce shock waves in a wider range of parameter space. A 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 two-dimensional accretion in Schwarzschild geometry. In the strong-viscosity limit, the shocks may be located farther out or disappear completely, as in the pseudo-Newtonian geometry.