  The subject of this dissertation consists in analyzing a recent proposition,
advanced by C.C.Barros, in which the non gravitational interactions can affect
the space-time metric as in gravity. In fact, in the context of the
Schwarzschild solution, the hydrogen atom is described in a completely new way
: instead of following the usual approach to describe the electron under the
Coulomb potential by using the minimal coupling, the "proton-electron"
interaction is rather incorporated in the metric. In this context, we reproduce
in this dissertation the same equations as predicted in Dirac theory for the
weak potential approximation. Contrary to the statement made by Barros,
claiming that he brought an insignificant correction to the electron levels, at
the end of our analysis, we assert that this new approach has the merit of
reproducing the relativistic spectrum as known in the Dirac theory. These
spectacular results incite us to wonder about the role of the Principle of
Equivalence in the foundations of the general theory of relativity.
