  The Lagrangian formulation of field theory does not provide any universal
energy-momentum conservation law in order to analize that in gravitation
theory. In Lagrangian field theory, we get different identities involving
different stress energy-momentum tensors which however are not conserved,
otherwise in the covariant multimomentum Hamiltonian formalism. In the
framework of this formalism, we have the fundamental identity whose restriction
to a constraint space can be treated the energy-momentum transformation law.
This identity remains true also for gravity. Thus, the tools are at hand to
investigate the energy-momentum conservation laws in gravitation theory. The
key point consists in the feature of a metric gravitational field whose
canonical momenta on the constraint space are equal to zero.
