  The Hamiltonian analysis for the Einstein's action in $ G\to 0 $ limit is
performed. Considering the original configuration space without involve the
usual $ADM$ variables we show that the version $ Gto 0 $ for Einstein's action
is devoid of physical degrees of freedom. In addition, we will identify the
relevant symmetries of the theory such as the extended action, the extended
Hamiltonian, the gauge transformations and the algebra of the constraints. As
complement part of this work, we develop the covariant canonical formalism
where will be constructed a closed and gauge invariant symplectic form. In
particular, using the geometric form we will obtain by means of other way the
same symmetries that we found using the Hamiltonian analysis.
