A numerical examination of an evolving black string horizon
  We use the numerical solution describing the evolution of a perturbed black string presented in Choptuik et al. (2003) to elucidate the intrinsic behavior of the horizon. It is found that by the end of the simulation, the affine parameter on the horizon has become very large and the expansion and shear of the horizon in turn very small. This suggests the possibility that the horizon might pinch off in infinite affine parameter. 
D. Garfinkle, L. Lehner, F. Pretorius