  We study the existence of smooth topological solitons and black strings as
locally-stable saddles of the Euclidean gravitational action of five
dimensional Einstein-Maxwell theory. These objects live in the Kaluza-Klein
background of four dimensional Minkowski with an $S^1$. We compute the
off-shell gravitational action in the canonical ensemble with fixed boundary
data corresponding to the asymptotic radius of $S^1$, and to the electric and
magnetic charges that label the solitons and black strings. We show that these
objects are locally-stable in large sectors of the phase space with varying
lifetime. Furthermore, we determine the globally-stable phases for different
regimes of the boundary data, and show that there can be Hawking-Page
transitions between the locally-stable phases of the topological solitons and
black strings. This analysis demonstrates the existence of a large family of
globally-stable smooth solitonic objects in gravity beyond supersymmetry, and
presents a mechanism through which they can arise from the black strings.
