Geometry of D1-D5-P bound states

Supersymmetric solutions of 6D supergravity (with two translation symmetries) can be written as a hyper-Kähler base times a 2D fiber. The subset of these solutions which correspond to true bound states of D1-D5-P charges give microstates of the 3-charge extremal black hole. To understand the characteristics shared by the bound states we decompose known bound state geometries into base-fiber form. The axial symmetry of the solutions make the base Gibbons-Hawking. We find the base to be actually 'pseudo-hyper-Kähler': The signature changes from (4,0) to (0,4) across a hypersurface. 2-charge D1-D5 geometries are characterized by a 'central curve' S1; the analogue for 3-charge appears to be a hypersurface that for our metrics is an orbifold of S1×S3.