%ABah, Ibrahima%ADey, Anindya%AHeidmann, Pierre%BJournal Name: Journal of High Energy Physics; Journal Volume: 2022; Journal Issue: 4 %D2022%I %JJournal Name: Journal of High Energy Physics; Journal Volume: 2022; Journal Issue: 4 %K %MOSTI ID: 10332870 %PMedium: X %TStability of topological solitons, and black string to bubble transition %XA bstract 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. %0Journal Article