This article introduces classical field theory in a curved spacetime background, using a scalar field as an example. The use of a general background metric enables defining the Hilbert stress-energy tensor. The canonical stress-energy tensor that was introduced in in article 49705 is associated with the translation symmetry of flat spacetime via Noether's first theorem, whereas the Hilbert stress-energy tensor arises naturally from the equation of motion for the metric field in general relativity. Article 32191 explains why these two differently-defined stress-energy tensors are consistent with each other.
