Smarr's Formula in Eleven-Dimensional Supergravity

We examine the Smarr formula in eleven-dimensional spacetime compactified on a general six-dimensional, Ricci-flat manifold. We show that non-zero mass for smooth and horizonless solutions can only be provided by cohomology. Furthermore, we confirm the result that there are no solitons without topology and prove the fact that Chern-Simons terms in the mass formula only appear in order to generate a purely topological integral.