Schwarzschild-like Topological Solitons

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.

Fuzzballs and Microstate Geometries: Black-Hole Structure in String Theory

“…Over the years, there has been some construction of non-supersymmetric microstate geometries, but these have often led to extremal, non-supersymmetric solutions, or solutions with very high angular momenta [79,[107][108][109][110][111][112][113][114][115]. However, the last year has seen some spectacular progress in the systematic construction of very interesting, non-supersymmetric microstate geometries [23,24,116,117]. These constructions demonstrate that many of the remarkable features of supersymmetric microstate geometries are shared by non-supersymmetric counterparts.…”

“…We believe that this is simply a technical problem. Indeed, the recent construction of non-BPS microstate geometries [116,117] achieves this paradigm beautifully, with topology created from cycles pinching off in both the compactification and space-time directions.…”

“…A recent breakthrough [116,117] 6 has led to a systematic construction of large families of non-BPS non-extremal, multi-bubbled microstate geometries. To solve the equations of motion, rather than the much simpler BPS equations, one must simplify the problem by imposing enough symmetry to reduce the equations to a two-dimensional problem.…”

“…It is unclear whether the coincidence of the fuzzball multipole moments to those of the black hole in the scaling limit is an artifact of extremal black hole, or is rather a universal feature that will apply also to microstates geometries for the Schwarzschild and Kerr black holes. The obvious next step is to build upon the results of [116,117] and construct and such microstate geometries and analyze their multipole moments.…”

“…The construction of microstate geometries is far from complete: every year, new classes of such geometries are constructed, or conjectured to exist. Indeed, the last year has seen a huge range of new possibilities [23,93,116,117,40,157].…”