  Radiation emitted from an accretion disk around a massive black hole is a
widely discussed model for the UV/soft X-ray excess emission observed in the
spectra of many AGN. A self-consistent calculation of the structure and the
emerging spectrum of geometrically thin alpha-accretion disks in AGN is
presented. The central object is assumed to be a Kerr black hole; full
relativistic corrections are included. The local dissipation of gravitational
energy is assumed to be entirely due to turbulence. Since these disks are
mainly supported by radiation pressure, the assumption that the viscous energy
production is proportional to the total pressure leads to diverging temperature
structures in the upper parts of the disk, where the total optical depths is
small. We therefore modify the standard expression for the turbulent viscosity
by taking into account the radiative energy loss of turbulent elements in an
optically thin regime. Compton scattering is treated in the Fokker-Planck
approximation using the Kompaneets oparator. The absorption cross section
contains only free-free processes for a pure hydrogen atmosphere. We present
several calculations for various parameters such as the accretion rate, the
viscosity parameter, the specific angular momentum of the black hole and the
inclination angle of the observer. The resulting temperature and density
profiles show that the disks are optically thick for Compton scattering and
effectively optically thin for most frequencies. This leads to spectra that are
diluted with respect to the photon number but contain a Comptonized high energy
tail in order to carry the required energy flux. In addition the electron
temperature deviates strongly from the equilibrium temperature. Therefore, the
model can in general account for the observed soft X--ray excess.
