Nonlinear Interactions Between Gravitational Radiation and Modified Alfven Modes in Astrophysical Dusty Plasmas

We present an investigation of nonlinear interactions between Gravitational Radiation and modified Alfv\'{e}n modes in astrophysical dusty plasmas. Assuming that stationary charged dust grains form neutralizing background in an electron-ion-dust plasma, we obtain the three wave coupling coefficients, and calculate the growth rates for parametrically coupled gravitational radiation and modified Alfv\'{e}n-Rao modes. The threshold value of the gravitational wave amplitude associated with convective stabilization is particularly small if the gravitational frequency is close to twice the modified Alfv\'en wave-frequency. The implication of our results to astrophysical dusty plasmas is discussed.