Dark matter cavity and amplification of gravitational waves

Abstract: The linearized Einstein theory in the approximately flat time-space is modified accounting for a massive graviton as a dark matter in the universe. On the basis of magnetic-type Maxwell- Proca -Vlasov equations, the interactions of the gravitoelectromagnetic fields (GEM), involving the vector potential, with gravitons (dark matter) dealing with resonant wave-particle and wave-wave one are studied. It is found that the behavior of the perturbed GEM fields and the perturbed matter density can be described by the nonlinear coupling Eqs.(4.6) and(4.7). It is shown that the perturbed field is instable with respect to the collapse, leading to enhancement of the GE field. In other words, the gravitational waves (GWs) are amplified and concurrently the cluster and cavity of the dark matter formed. And it is referred that the lower limit for graviton mass is $M_{gr}^\geqslant 10^{- 50}(g)$ by the condition to exist stable longitudinal mode.