When luminosity of black hole accretion disks is greater than 0.06 Eddington luminosity (L ≥ 0.06LE), according to standard disk model, the inner region of these disks is radiation-pressure dominated (RPD) and unstable in thermal and viscous modes. Whereas this object conflicts with the observations, if 0.01LE ≤ L ≤ 0.5LE. Thus, the change of viscosity or considering relativistic corrections that are essential in realistic black hole accretion disks may solve this problem between theory and observation. An explanation by taking into account the effect of black hole spin with the presence of different viscosities on the secular and thermal instabilities in geometrically thin optically thick accretion disks is presented. In order to consider the effects of spin and general relativity, kerr space-time is used. A diffusive form of viscous stress tensor, a new form of fully relativistic shear stress tensor that is not used so far, power law, and parametric viscosity are considered. Investigations have been done in some parameters of viscosity and some values of spin. We conclude that the type of viscosity is effective in stabilization of the disk, whereas spin has no effect. Increasing stability or instability in the disk can be caused by spin, which this behavior is related to the type of viscous parameter. Thereby, spin can be effective on the temperature, accretion rate, and in the luminosity of the system.
