Bubble Bag End: A Bubbly Resolution of Curvature Singularity

TL;DR

This paper constructs smooth, charged bubbling solitons in four-dimensional spacetime that resolve curvature singularities by topological cycle blow-ups, extending beyond supersymmetric frameworks.

Contribution

It introduces a new class of non-supersymmetric, non-extremal bubbling geometries that resolve curvature singularities through topological transitions.

Findings

Bubbling solitons are smooth and ultra-compact.

Solutions can approximate singular spacetimes arbitrarily closely.

First classical resolution of non-supersymmetric curvature singularities.

Abstract

We construct a family of smooth charged bubbling solitons in $\mathbb{M}^4 \times$T$^2$, four-dimensional Minkowski with a two-torus. The solitons are characterized by a degeneration pattern of the torus along a line in $\mathbb{M}^4$ defining a chain of topological cycles. They live in the same parameter regime as non-BPS non-extremal four-dimensional black holes, and are ultra-compact with sizes ranging from miscroscopic to macroscopic scales. The six-dimensional framework can be embedded in type IIB supergravity where the solitons are identified with geometric transitions of non-BPS D1-D5-KKm bound states. Interestingly, the geometries admit a minimal surface that smoothly opens up to a bubbly end of space. Away from the solitons, the solutions are indistinguishable from a new class of singular geometries. By taking a limit of large number of bubbles, the soliton geometries can be matched arbitrarily close to the singular spacetimes. This provides the first classical resolution of a curvature singularity beyond the framework of supersymmetry and supergravity by blowing up topological cycles wrapped by fluxes at the vicinity of the singularity.