  The proposal of this work is to provide an answer to the following question:
is it possible to treat the metric of space-time - that in General Relativity
(GR) describes the gravitational interaction - as an effective geometry? In
other words, to obtain the dynamics of the metric tensor as a consequence of
the dynamics of other fields. In this work we will use a slight modfication of
the non-linear equation of motion of a spinor field proposed some years ago by
Heisenberg, although in a completely distinct context, to obtain a field theory
that provides a framework equivalent to the way GR represents the gravitational
interaction. In particular we exhibit a solution of the equations of motion
that represents the gravitational field of a compact object and compare it with
the corresponding Schwarzschild solution of General Relativity.
