  We apply the ultrarelativistic boosting procedure to map the metric of
Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime
plus a shock-wave singularity located on a null hypersurface, by exploiting the
picture of the embedding of an hyperboloid in a five-dimensional Minkowski
spacetime. After reverting to the usual four-dimensional formalism, we also
solve the geodesic equation and evaluate the Riemann curvature tensor of the
boosted Schwarzschild-de Sitter metric by means of numerical calculations,
which make it possible to reach the ultrarelativistic regime gradually by
letting the boost velocity approach the speed of light. Eventually, the
analysis of the Kretschmann invariant (and of the geodesic equation) shows the
global structure of space- time, as we demonstrate the presence of a "scalar
curvature singularity" within a 3-sphere and find that it is also possible to
define what we have called "boosted horizon", a sort of elastic wall where all
particles are surprisingly pushed away. This seems to suggest that such
"boosted geometries" are ruled by a sort of "antigravity effect" since all
geodesics seem to refuse entering the "boosted horizon" and are "reflected" by
it, even though their initial conditions are aimed at driving the particles
towards the "boosted horizon" itself.
