Gravitational polarization of the quantum vacuum caused by two point-like bodies

ABSTRACT In a recent paper, quantum vacuum was considered as source of gravity, and the simplest, phenomenon, gravitational polarization by an immersed point-like body, studied. this we have derived effective charge density vacuum, caused two bodies. Among others, obtained result proves that can regions with negative density. Hence, ‘ocean’ in which all matter Universe is immersed, acts complex fluid very variable might include both positive densities; crucial prediction be tested within Solar system. general case ${N \ge {\rm{3}}}$ bodies, analytical solutions are not possible, use numerical methods inevitable. The key point appropriate method, for calculation induced N description galaxies, without involvement dark or modification gravity. development such valuable previous (and study achieved) understanding impact two-body