  We show that any generally covariant coupling of matter fields to gravity
gives rise to a conserved, on-shell symmetric energy-momentum tensor equivalent
to the canonical energy-momentum tensor of the flat-space theory. For matter
fields minimally coupled to gravity our algorithm gives the conventional
Belinfante tensor. We establish that different matter-gravity couplings give
metric energy-momentum tensors differing by identically conserved tensors. We
prove that the metric energy-momentum tensor obtained from an arbitrary gravity
theory is on-shell equivalent to the canonical energy-momentum tensor of the
flat-space theory.
