Calculation of the relativistic bulk tensor and shear tensor of relativistic accretion flows in the Kerr metric.

In this paper, we calculate the relativistic bulk tensor and shear tensor of the relativistic accretion ows in the Kerr metric, overall and without any approximation. We obtain the relations of all components of the relativistic bulk and shear tensor in terms of components of fourvelocity and its derivatives, Christoffel symbols and metric components in the BLF. Then, these components are derived in the equatorial plane. To see the behavior of the relativistic bulk tensor and shear tensor in the relativistic accretion disks around the rotating black holes, we introduce a radial form for the radial component of the fourvelocity in the LNRF; therefore, all components of the bulk and shear tensor are derived in the BLF. Figures of nonzero components of the bulk tensor and shear tensor are shown for some states. We use the radial model to study the importance and in uence of the relativistic bulk tensor in the accretion disks around the rotating black holes. Also, we see that in some cases bulk tensor may be important and comparable with the shear tensor. Especially, we see that bulk tensor in the inner radii is more important.