The domain of outer communication of an asymptotically flat spactime must be simply connected. In five dimensions, this still allows for the possibility of an arbitrary number of 2-cycles supported by magnetic flux carried by Maxwell fields. As a result, stationary, asymptotically flat, horizonless solutions—“gravitational solitons”—may exist with non-vanishing mass, charge, and angular momenta. These gravitational solutions satisfy a Smarr-like relation, as well as a first law of mechanics. Furthermore, the presence of solitons leads to new terms in the well-known first law of black hole mechanics for spacetimes containing black hole horizons and non-trivial topology in the exterior region. I outline the derivation of these results and consider an explicit example in five-dimensional supergravity.
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