where d x α α β β = ι ι ∂ ∂ α α d x β β = ι ι ∂ ∂ α α ι ι ∂ ∂ β β d 4 x denotes interior product, generalizes to an arbitrary vector field ξ ξ the so-called above Komar superpotential, which was originally derived for timelike Killing vector fields.