Smarr's Formula in Eleven-Dimensional Supergravity

TL;DR

This paper investigates the Smarr formula in eleven-dimensional supergravity, demonstrating that mass in smooth, horizonless solutions arises solely from cohomology and emphasizing the topological nature of Chern-Simons contributions.

Contribution

It proves that non-zero mass solutions require non-trivial topology and clarifies the topological origin of Chern-Simons terms in the mass formula.

Findings

Mass in smooth, horizonless solutions is due to cohomology.

No solitons exist without topology.

Chern-Simons terms contribute only topologically.

Abstract

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.