  In this paper, we first review Huei's formulation in which it is shown that
the linearized Einstein equations can be written in the same form as the
Maxwell equations. We eliminate some imperfections like the scalar potential
which is ill linked to the electric-type field, the Lorentz-type force which is
obtained with a time independence restriction and the undesired factor 4 which
appears in the magnetic-type part. Second, from these results and in the light
of a recent work by C.C. Barros, we propose an extension of the equivalence
principle and we suggest a new interpretation for Einstein's equations by
showing that the electromagnetic Maxwell equations can be derived from a new
version of Einstein's ones.
