Its generalization in general relativity is L ^ ^ G R [ f ] = p α α ∂ ∂ f ∂ ∂ x α α − − Γ Γ α α β β γ γ p β β p γ γ ∂ ∂ f ∂ ∂ p α α = C [ f ] , where Γ βγ is the Christoffel symbol of the second kind (this assumes there are no external forces, so that particles move along geodesics in the absence of collisions), with the important subtlety that the density is a function in mixed contravariant-covariant (x, p i) phase space as opposed to fully contravariant (x, p) phase space.