  We show that in the D1-D5 system with angular momentum, there can be
localised tachyonic winding string modes in the interior of the spacetime even
if we choose a spin structure which preserves supersymmetry in the asymptotic
region. We consider cases where the tachyonic region extends outside the event
horizon, and argue that the natural endstate of tachyon condensation in almost
all cases is one of the solitonic solutions which correspond to special
microstates of the D1-D5 system.
