  Results are presented from a time--dependent, numerical investigation of
spherical accretion onto black holes, within the framework of relativistic
radiation hydrodynamics. We have studied the stability of self--consistent,
stationary solutions of black hole accretion with respect to thermal and
radiative perturbations and also the non--linear evolution of unstable, high
temperature models, heated by the hard radiation produced by the accretion flow
itself in the inner region near to the horizon. In some cases, a hydrodynamic
shock forms at around $10^3$--$10^4$ Schwarzschild radii, where Compton heating
exceeds radiative cooling. The calculations were made using a suitably designed
radiation hydrodynamics code, in which radiative transfer is handled by means
of the PSTF moment formalism and which contains an original treatment of the
radiation temperature equation.
