In this work we revisit the study of the gravitational interaction in the context of the special
theory of relativity. It is found that, as long as the equivalence principle is respected, a
relativistic nonlinear energy conservation theorem arises in a natural way. We interpret that this
nonlinear conservation law stresses the nonlinear character of the gravitational interaction. The
theorem reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low
energy limit, but also allows to derive some standard results of post-Newtonian gravity, such as the
formula of the gravitational redshift. Guided by this conservation law, we develop a Lagrangian
formalism for a particle in a gravitational field. We realize that the Lagrangian can be written in
an explicit covariant fashion, and turns out to be the geodesic Lagrangian of a curved Lorentzian
manifold. Therefore, any attempt to describe gravity within the special theory, leads outside their
own domains t…