Magnetic Charge Can Locally Stabilize Kaluza-Klein Bubbles

We construct a new 2-parameter family of static topological solitons in 5D minimal supergravity which are endowed with magnetic charge and mass. The solitons are asymptotically ${\mathbb R}^4\times S^1$, where the radius of the $S^1$ has a lower bound $R_s\ge R_{min}$. Setting up initial data on a Cauchy slice at a moment of time symmetry, we demonstrate that if $R_s>R_{min}$ these solitons correspond to a perturbatively stable "small" static bubble as well as an unstable "large" static bubble, whereas if $R_s<R_{min}$ there are no static bubbles. The energetics and thermodynamics of the magnetic black string are then discussed and it is shown that the locally stable bubble is the end point of a phase transition for an appropriate range of black string parameters.