More Bubbling Solutions

TL;DR

This work constructs and analyzes a broad family of asymptotically flat, smooth, horizonless bubbling solutions in N=1 five-dimensional supergravity by lifting four-dimensional multi-center BPS configurations to five dimensions in the decompactification limit. The method relies on D6/anti-D6 centers with world-volume flux in a Calabi–Yau compactification, followed by a careful rescaling to obtain a well-defined five-dimensional description, yielding geometries with many bubbles and controllable charges. The authors compute the conserved charges, map 4D to 5D charges, and examine asymptotics, the no-CTC condition, and the presence of a possible AdS$_2\times$S$^3$ throat, showing that a throat arises only when the total charge matches a classical black hole; near each center the solution is smooth, with bubbling two-cycles supported by flux. The results illuminate the microstate/“fuzzball” perspective for black holes in Calabi–Yau compactifications and discuss degeneracies, throat structure, and potential holographic interpretations, outlining future directions for understanding entropy from non-compact degrees of freedom.

Abstract

In this note we construct families of asymptotically flat, smooth, horizonless solutions with a large number of non-trivial two-cycles (bubbles) of N=1 five-dimensional supergravity with an arbitrary number of vector multiplets, which may or may not have the charges of a macroscopic black hole and which contain the known bubbling solutions as a sub-family. We do this by lifting various multi-center BPS states of type IIA compactified on Calabi-Yau three-folds and taking the decompactification (M-theory) limit. We also analyse various properties of these solutions, including the conserved charges, the shape, especially the (absence of) throat and closed timelike curves, and relate them to the various properties of the four-dimensional BPS states. We finish by briefly commenting on their degeneracies and their possible relations to the fuzzball proposal of Mathur et al.