Structure of Six-Dimensional Microstate Geometries

TL;DR

This paper analyzes the topological structure of six-dimensional microstate geometries related to D1-D5-P black holes, showing that non-trivial topology is necessary for smooth, horizonless solutions and applying topological arguments to various examples.

Contribution

It extends the topological analysis of microstate geometries from five to six dimensions, clarifying the role of topology in horizonless solutions without Chern-Simons terms.

Findings

Smooth, horizonless solutions require non-trivial topology.

Topological arguments apply to various microstate examples.

Smarr formula consistency across different microstate configurations.

Abstract

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.