  The construction of neutral black hole microstates is an important problem,
with implications for the information paradox. In this paper we conjecture a
construction of non-supersymmetric supergravity solutions describing D-brane
configurations which carry mass and angular momentum, but no other conserved
charges. We first study a classical string solution which locally carries
dipole winding and momentum charges in two compact directions, but globally
carries no net winding or momentum charge. We investigate its backreaction in
the D1-D5 duality frame, where this object becomes a supertube which locally
carries oscillating dipole D1-D5 and NS1-NS5 charges, and again carries no net
charge. In the limit of an infinite straight supertube, we find an exact
supergravity solution describing this object. We conjecture that a similar
construction may be carried out based on a class of two-charge
non-supersymmetric D1-D5 solutions. These results are a step towards
demonstrating how neutral black hole microstates may be constructed in string
theory.
