Fuzzball geometries and higher derivative corrections for extremal holes

2-charge D1-D5 microstates are described by geometries which end in 'caps' near r = 0; these caps reflect infalling quanta back in finite time. We estimate the travel time for 3-charge geometries in 4D, and find agreement with the dual CFT. This agreement supports a picture of 'caps' for 3-charge geometries. We argue that higher derivative corrections to such geometries arise from string winding modes. We then observe that the 'capped' geometries have no non-contractible circles, so these corrections remain bounded everywhere and cannot create a horizon or singularity. (c) 2006 Elsevier B.V. All rights reserved.