Stability of topological solitons, and black string to bubble transition

Abstract

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.

arXiv comment26 pages plus appendices, 4 figures. Minor edits in v2

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• Imaging Topological Solitons: the Microstructure Behind the Shadow
• Cavity effect in the quasinormal mode spectrum of topological stars
• Non-BPS Bubbling Geometries in AdS${}_3$
• Gravitoelectromagnetic coupled perturbations and quasinormal modes of a charged black hole with scalar hair
• Solitonic Excitations in AdS2
• Quasinormal modes of a charged black hole with scalar hair
• Extreme mass ratio inspirals around topological stars
• Neutralizing Topological Obstructions to Bubbles of Nothing