List of Footnotes

1 Our conventions are: k k k j ∇iv = ∂iv + Γ ijv, with k 1 kl Γ ij = 2𝔥 [∂j𝔥il + ∂i𝔥jl − ∂l𝔥ij]. The Riemann tensor is defined by k k l (∇i∇j − ∇j∇i )v = R lijv, so that k k k k m k m R lij = ∂iΓ lj − ∂jΓ li + Γ imΓ lj − Γ jm Γ li. The Ricci tensor is m Rij = R imj.