  We show that the symplectic current obtained from the boundary term, which
arises in the first variation of a local diffeomorphism invariant action, is
covariantly conserved for any gravity theory described by that action.
Therefore, a Poincare invariant 2-form can be constructed on the phase space,
which is shown to be closed without reference to a specific theory. Finally, we
show that one can obtain a charge expression for gravity theories in various
dimensions, which plays the role of the Abbott-Deser-Tekin (ADT) charge for
spacetimes with non-constant curvature backgrounds, by using the diffeomorphism
invariance of the symplectic 2-form. As an example, we calculate the conserved
charges of some solutions of New Massive Gravity (NMG) and compare the results
with the previous works.
