The problem of radiative instability of homogeneous rotating partially ionized plasma incorporating viscosity, porosity, and electron inertia in the presence of a magnetic field is investigated. A general dispersion relation is obtained using normal mode analysis with the help of relevant linearized perturbation equations of the problem. The modified Jeans criterion of instability is obtained. The conditions of Jeans instabilities are discussed in the different cases of interest. It is found that the simultaneous effect of viscosity, rotation, finite conductivity, and porosity of the medium does not essentially change the Jeans criterion of instability. It is also found that the presence of arbitrary radiative heat-loss function and thermal conductivity modified the conditions of Jeans instability for longitudinal propagation. It is found that, for longitudinal propagation, the conditions of radiative instability are independent of magnetic field, viscosity, rotation, finite electrical resistivity, and electron inertia, but for the transverse mode of propagation it depends upon finite electrical resistivity and strength of magnetic field and is independent of viscosity, electron inertia, and rotation. From the curves we find that viscosity has a stabilizing effect on the growth rate of instability but the thermal conductivity and density-dependent heat-loss function has a destabilizing effect on the instability growth rate.
