Notice that the condition of Tαβ being divergence-free depends on the metric gαβ itself, which is not known before actually solving the nonlinear wave equation (4.5View Equation), and the latter, in turn, depends on T αβ. Therefore, one cannot specify Tαβ by hand, except in the vacuum case, Tαβ = 0, or in the case Tαβ = − Λg αβ with Λ the cosmological constant. In the more general case, the stress-energy tensor has to be computed from a diffeomorphism-independent action for the matter fields and one has to consistently solve the coupled Einstein-matter system.