On the energy-momentum tensor

We clarify the relation among canonical, metric and Belinfante's energy-momentum tensors for general tensor field theories. For any tensor field T, we define a new tensor field $\til {\bm T}$, in terms of which the Belinfante tensor is readily computed. We show that the latter is the one that arises naturally from Noether Theorem for an arbitrary spacetime and it coincides on-shell with the metric one.