Abstract
We construct a family of smooth charged bubbling solitons in mathbbm{M} 4×T2, four-dimensional Minkowski with a two-torus. The solitons are characterized by a degeneration pattern of the torus along a line in mathbbm{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 ultracompact 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.
Highlights
The resolution of singularities in general relativity (GR) is of paramount interest as it holds the key to uncovering fundamental aspects of black holes and big bang initial conditions
We have shown in [19] that the Weyl formalism can be generalized to this context where the non-linear Einstein equations, with an appropriate Weyl ansatz, can be reduces to a set of linear equations that allows us to superpose different species of sources
This system can be embedded in IIB supergravity where the sources in our constructions correspond to non-BPS bound states of D1-D5-KKm systems
Summary
The resolution of singularities in general relativity (GR) is of paramount interest as it holds the key to uncovering fundamental aspects of black holes and big bang initial conditions. In classical theories of gravity, it is interesting to ask whether there exist such coherent states that resolve singularities These would correspond to solitons of the nonlinear field equations, i.e. smooth asymptotically flat stationary solutions with finite energy. The results in these work lead to the theorem in four dimensions: If a solution is asymptotically flat, topologically trivial and globally stationary (i.e. admits an everywhere timelike Killing vector field) it must be flat space. This is a no-go theorem for solitons that are topologically trivial.
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