Gravitational Instability of Dusty Plasma with Radiative Process

The gravitational instability of infinite homogeneous magnetized dusty plasma with radiative process is studied with the help of relevant dusty magnetohydrodynamic (MHD) equations using normal mode analysis. The dispersion relation is obtained with radiative pressure and magnetic field, which is discussed for the transverse and longitudinal mode of propagations. The improvement in the Jeans condition of instability due to dust, magnetic field and radiative pressure is discussed. We find that in transverse mode of propagation the condition of Jeans instability of dusty plasma is modified by magnetic field and radiative pressure. In case of longitudinal mode it is unaffected by magnetic field as this mode provides the Alfven mode separately with the gravitational mode.