Schwarzschild-like Topological Solitons

TL;DR

This paper constructs novel six-dimensional topological solitons in gravity supported by electromagnetic flux, which can be uplifted to string theory and resemble black holes but are smooth, horizonless, and ultra-compact with tunable charges.

Contribution

It introduces the first class of gravitational topological solitons supported by internal flux with zero net charge, including BPS and anti-BPS bound states, extending the landscape of smooth horizonless solutions.

Findings

Solutions are asymptotic to a torus fibration over Minkowski space.

They can carry arbitrary D1-D5 charges with zero net charge.

They are ultra-compact, with a size 1.52 times the Schwarzschild radius.

Abstract

We construct the first class of topological solitons in gravity that are supported by internal electromagnetic flux with vanishing net charges. The solutions are obtained in a six-dimensional Einstein-Maxwell theory with a three-form flux, and admit an uplift to type IIB supergravity on T$^4$. They are asymptotic to a torus fibration over four-dimensional Minkowski spacetime. An interesting class corresponds to solitons with a BPS particle and its anti-BPS partner held apart by a vacuum bubble. In type IIB, they correspond to bound states of BPS and anti-BPS D1-D5 extremal black holes. These metrics are a particular limit of a larger class of axially symmetric metrics that we construct and that describe smooth horizonless topological solitons. They correspond to bound states of three non-BPS bubbles on a line. An important achievement is that the outer bubbles can carry arbitrary D1-D5 charges that we can tune to vanishing net charges. We discuss their properties and compare them to a four-dimensional Schwarzschild black hole of the same mass. We show that they have a long throat with a large redshift, and that they are ultra-compact with a characteristic size of 1.52 times the Schwarzschild radius.