Shear Tensor and Dynamics of Relativistic Accretion Disks around Rotating Black Holes

In this paper we solve the hydrodynamical equations of optically thin, steady state accretion disks around Kerr black holes. Here, fully general-relativistic equations are used. We use a new method to calculate the shear tensor in the LNRF (Locally Non-Rotating Frame), BLF (Boyer-Lindquist Frame), and FRF (Fluid Rest Frame). We show that two components of shear tensor in the FRF are nonzero (in previous works only one nonzero component was assumed). We can use these tensors in usual transonic solutions and usual causal viscosity, but we derive solutions analytically by some simplifications. Then, we can calculate the four-velocity and density in all frames, such as the LNRF, BLF, and FRF.