Magnetic Charge Can Locally Stabilize Kaluza-Klein Bubbles

TL;DR

This paper constructs a new family of magnetic charged static solitons in 5D supergravity, revealing conditions for their stability and their role as end points of phase transitions involving black strings.

Contribution

It introduces a novel 2-parameter family of magnetic charged solitons in 5D supergravity with stability analysis and phase transition implications.

Findings

Stable small static bubbles exist for radii above a minimum threshold.

Large static bubbles are unstable and exist only above the minimum radius.

The stable bubble can serve as the end point of a phase transition from black strings.

Abstract

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.