  Strong anti-gravity is the vanishing to all orders in Newton's constant of
the net force between two massive particles at rest. We study this phenomenon
and show that it occurs in any effective theory of gravity which is obtained
from a higher-dimensional model by compactification on a manifold with flat
directions. We find the exact solution of the Einstein equations in the
presence of a point-like source of strong anti-gravity by dimensional reduction
of what is a shock-wave solution in the higher-dimensional model. (Latex file,
no macros, figures not included)
