In fact, as is well known, the Einstein–Hilbert action for general relativity was first formulated purely in terms of the spacetime metric g μ μ ν ν . In the Palatini variational method one takes as independent field variables not only the ten components g μ μ ν ν but also the forty components of the affine connection Γ Γ β β μ μ α α , assuming, a priori, no dependence of the Γ Γ β β μ μ α α from the g μ μ ν ν and their derivatives.