Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\rightarrow 0$ limit

In this paper the Dirac and Faddeev-Jackiw formulation for Einstein's theory in the $G \rightarrow 0$ limit is performed; the fundamental Dirac's and Faddeev-Jackiw brackets for the theory are obtained. First, the Dirac brackets are constructed by eliminating the second class constraints remaining the first class ones, then we fix the gauge and we convert the first class constraints into second class constraints and the new fundamental Dirac's brackets are computed. Alternatively, we reproduce all relevant Dirac's results by means of the symplectic method. We identify the Faddeev-Jackiw constraints and we prove that the Dirac and the Faddeev-Jackiw brackets coincide to each other. .