Abstract
Large, localized variations of light scalar fields tend to collapse into black holes, dynamically “censoring” distant points in field space. We show that in some cases, large scalar excursions in asymptotically flat spacetimes can be UV-completed by smooth Kaluza-Klein bubble geometries, appearing to circumvent 4d censorship arguments. However, these spacetimes also exhibit classical instabilities related to the collapse or expansion of a bubble of nothing, providing a different censorship mechanism. We show that the Kerr family of static KK bubbles, which gives rise to an infinite scalar excursion upon dimensional reduction, is classically unstable. We construct a family of initial data in which the static bubbles sit at a local maximum of the energy, and we give a general argument that such a property indeed indicates mechanical instability in gravity. We also discuss the behavior of wound strings near a bubble, a local probe of the large traversal through moduli space.
Highlights
We will show that some of the 4d configurations used in the analysis of [4] can be UVcompleted by static Kaluza-Klein (KK) geometries
We show that in some cases, large scalar excursions in asymptotically flat spacetimes can be UV-completed by smooth KaluzaKlein bubble geometries, appearing to circumvent 4d censorship arguments
The study of inflationary models with large scalar field excursions in time [14] and the difficulties associated with finding long flat directions in string theory [15] originally motivated the Weak Gravity Conjecture (WGC), and the implications of the WGC for scalar field ranges / large moduli spaces is an active area of study [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
Summary
Instead of cutting off the curvature singularity with a finite-radius source, the metric+scalar (2.1) can be smoothly completed in Kaluza-Klein theory. The relevant KK solution was constructed in [37] by adding a Lorentzian time direction to 4d Euclidean Schwarzschild (ES) gravitational instanton [38]. We refer to this solution as the ES bubble. The ES bubble is a nonsingular 5d realization of a 4d scalar with a large, localized, static ∆φ. Similar relationships of this type have been noted in the literature. Kastor and Traschen found that 4D cosmological spacetimes related to the Buchdahl spacetimes may be obtained from dimensional reduction [39], while Garriga [40] and Brown and Dahlen [41] have shown the singular Hawking-Turok instanton [42] is related by dimensional reduction to the nonsingular 5d Witten BON instanton
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