  It is known that the canonical quantization of general relativity leads to a
non-renormalizable theory, which however with the modern tools of effective
field theories it is possible to make well-defined at low energies. What is
emerging nowadays is that recovering general relativity from the classical
limit of scattering amplitudes seems more efficient than actually solve the
Einstein equations. The thesis then aims to explore the state-of-the-art
strategies to recover classical gravitational observables from quantum
computations and apply them in order to reconstruct the
Reissner-Nordstr\"om-Tangherlini solution, which is the generalization to
arbitrary dimensions of the Reissner-Nordstr\"om one, from the classical limit
of scattering amplitudes of charged scalars. In the first part of the thesis,
we recover the most generic energy-ordered effective action which is compatible
with the symmetries of the theory, and then we discuss the classical limit from
which it is possible to obtain back classical gravitational observables out of
quantum computations. The state-of-the-art techniques to extract the classical
contributions out of graviton emission amplitudes are reviewed, and they are
applied to the context of a theory which is also coupled to the electromagnetic
field. Since divergences arise in four and five dimensions it is crucial to
define non-minimal couplings with the purpose of canceling such singularities
and obtaining finite results. In the end, the considerations employed in the
metric case are used to recover the electromagnetic potential associated to the
black hole solution through the classical limit of photon emission processes.
Also in this case there appear divergences that have to be renormalized. One of
the most important outcomes is that the counter-terms that have to be fixed in
order to eliminate the poles are the same throughout the theory.
