“…More precisely, the equivalence principle suggests to only take the metric as dynamical variable [76] representing the gravitational field (to which matter then couples universally), whereas diffeomorphism invariance, derivability from an invariant Lagrangian (alternatively: local energy-momentum conservation in the sense of covariant divergencelessness), dependence of the equations on the metric up to at most second derivatives, and, finally, four-dimensionality lead uniquely to the left-hand side of Einstein's equation, including a possibly non-vanishing cosmological constant [54]. Here we will review how this 'deduction' works in the Hamiltonian setting on phase space T * Riem(Σ), which goes back to [40,41,51,74].…”