  We outline a systematic procedure to obtain horizonless microstate geometries
that have the same charges as three-charge five-dimensional black holes with a
macroscopically-large horizon area and an arbitrarily-small angular momentum.
There are two routes through which such solutions can be constructed: using
multi-center Gibbons-Hawking (GH) spaces or using superstratum technology. So
far the only solutions corresponding to microstate geometries for black holes
with no angular momentum have been obtained via superstrata, and multi-center
Gibbons-Hawking spaces have been believed to give rise only to microstate
geometries of BMPV black holes with a large angular momentum. We perform a
thorough search throughout the parameter space of smooth horizonless solutions
with four GH centers and find that these have an angular momentum that is
generally larger than 80% of the cosmic censorship bound. However, we find that
solutions with three GH centers and one supertube (which are smooth in
six-dimensional supergravity) can have an arbitrarily-low angular momentum. Our
construction thus gives a recipe to build large classes of microstate
geometries for zero-angular-momentum black holes without resorting to
superstratum technology.
