  The thesis is divided into two parts. In the first part the low-energy limit
of quantum gravity is analysed, whereas in the second we deal with the
high-energy domain. In the first part, by applying the effective field theory
point of view to the quantization of general relativity, detectable, though
tiny, quantum effects in the position of Newtonian Lagrangian points of the
Earth-Moon system are found. In order to make more realistic the quantum
corrected model proposed, the full three-body problem where the Earth and the
Moon interact with a generic massive body and the restricted four-body problem
involving the perturbative effects produced by the gravitational presence of
the Sun in the Earth-Moon system are also studied. After that, a new quantum
theory having general relativity as its classical counterpart is analysed. By
exploiting this framework, an innovative interesting prediction involving the
position of Lagrangian points within the context of general relativity is
described. Furthermore, the new pattern provides quantum corrections to the
relativistic coordinates of Earth-Moon libration points of the order of few
millimetres. The second part of the thesis deals with the Riemannian curvature
characterizing the boosted form assumed by the Schwarzschild-de Sitter metric.
The analysis of the Kretschmann invariant and the geodesic equation shows that
the spacetime possesses a "scalar curvature singularity" within a 3-sphere and
that it is possible to define what we here call "boosted horizon", a sort of
elastic wall where all particles are surprisingly pushed away, suggesting that
such "boosted geometries" are ruled by a sort of "antigravity effect".
Eventually, the equivalence with the coordinate shift method is invoked in
order to demonstrate that all $\delta^2$ terms appearing in the Riemann
curvature tensor give vanishing contribution in distributional sense.
