Stationary accretion in the inner region of the disk is possible only for one definite value of the viscosity: |η c\,=\,4/9mp/σ Tc| A linear stability theory is constructed for stationary disk accretion on to black holes. The inner region of the disk, where radiation pressure dominates, is unstable against small perturbations. Growing short wave perturbations take the form of travelling concentric waves. For long wavelengths there are two branches of growing standing waves. The growth rate of one branch decreases rapidly with increasing wavelength; its asymptotic behaviour was found previously by Lightman & Eardley. The growth rate of the other branch increases to a constant limit as wavelength increases; this branch is the thermal instability of disk accretion. The above instabilities can explain the observed variability of radiation from binary X-ray sources, galactic nuclei and quasars, assuming these objects really do contain accreting black holes.
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Shakura et al. (1976) studied this question.