The effect of negative mass in gravitating systems

The effect of the negative effective mass emerging in the gravitating core-spring-shell system is considered. The effect appears when the entire system is exerted on the external harmonic force and the frequency of external force approaches the critical frequency ω from above. The critical frequency ω depends on the density of the self-gravitating system only. The scaling law predicting the value of ω for condensed phases is derived as ω0=A15ω~, where A is the atomic weight and ω~ is the fundamental frequency. The characteristic fundamental time scale corresponding to this frequency is close to the typical lifetime scale of the trapped atoms of antihydrogen. The generalisation of the effect for the Coulomb-like forces is reported.