Global Solutions of Viscous Transonic Flows in Kerr Geometry I: Weak Viscosity Limit

We present fully general relativistic equations governing viscous transonic flows in vertical equilibrium in Kerr geometry. We find the complete set of global solutions (both for Optically thick and optically thin flows) in the weak viscosity limit. We show that for a large region of parameter space, centrifugal pressure supported standing shocks can form in accretion and winds very close to the black hole horizon, both for co-rotating and contra-rotating flows. We compute the nature of the shear tensor for complete transonic solutions and discuss the consequences of its reversal properties.