Geometry of D1–D5–P bound states Original Research Article

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 image to image across a hypersurface. 2-charge D1–D5 geometries are characterized by a ‘central curve’ image; the analogue for 3-charge appears to be a hypersurface that for our metrics is an orbifold of image.