  We show that the `instantonic' soliton of five-dimensional Yang-Mills theory
and the closely related BPS monopole of four-dimensional Yang-Mills/Higgs
theory continue to be exact static, and stable, solutions of these field
theories even after the inclusion of gravitational, electromagnetic and, in the
four-dimensional case, dilatonic interactions, provided that certain
non-minimal interactions are included. With the inclusion of these
interactions, which would be required by supersymmetry, these exact
self-gravitating solitons saturate a gravitational version of the Bogomol'nyi
bound on the energy of an arbitrary field configuration.
