  We present a general linear dispersion relation which describes the coupled
behavior of magnetorotational, photon bubble, and convective instabilities in
weakly magnetized, differentially rotating accretion disks. We presume the
accretion disks to be geometrically thin and supported vertically by radiation
pressure. We fully incorporate the effects of a nonzero radiative diffusion
length on the linear modes. In an equilibrium with purely vertical magnetic
field, the vertical magnetorotational modes are completely unaffected by
compressibility, stratification, and radiative diffusion. However, in the
presence of azimuthal fields, which are expected in differentially rotating
flows, the growth rate of all magnetorotational modes can be reduced
substantially below the orbital frequency. This occurs if diffusion destroys
radiation sound waves on the length scale of the instability, and the magnetic
energy density of the azimuthal component exceeds the non-radiative thermal
energy density. While sluggish in this case, the magnetorotational instability
still persists and will still tap the free energy of the differential rotation.
Photon bubble instabilities are generically present in radiation pressure
dominated flows where diffusion is present. We show that their growth rates are
limited to a maximum value which is reached at short wavelengths where the
modes may be viewed as unstable slow magnetosonic waves. We also find that
vertical radiation pressure destabilizes upward propagating fast waves, and
that Alfv\'en waves can be unstable. These instabilities typically have smaller
growth rates than the photon bubble/slow modes. We discuss how all these modes
behave in various regimes of interest, and speculate how they may affect the
dynamics of real accretion disk flows.
