We consider the interaction of gravitational fields (including “gravitoelectromagnetism”) with interstellar matter dealing with resonant wave-particle and wave-wave interactions on the basis of magnetic-type Maxwell-Vlasov equations. It is found that the behavior of the perturbed GEM fields, the perturbed density and self-generated gravitomagnetic field with very low frequency, can be described by the nonlinear coupling Eqs. (98–100). Numerical results show that they may collapse. In other words, due to self-focusing, a stronger GEM fields magnified up to 103 times, could be produced; they are the GEM cavitons, describing gravity shielding and filament effects. And the self-generated gravitomagnetic field is concurrently focused by the background material to a small space where it may be detected.