Trapped surfaces in the Schwarzschild geometry and cosmic censorship

We prove that in extended Schwarzschild spacetime there exists a family of Cauchy surfaces which come arbitrarily close to the black-hole singularity at r=0 but are such that there do not exist any outer trapped surfaces lying within the past of any of these Cauchy surfaces. We argue that, in any spherically symmetric spacetime describing gravitational collapse to a Schwarzschild black hole, it should be possible to choose a spacelike slicing by Cauchy surfaces which terminates when a singularity (outside the matter) is reached, such that the region of the spacetime covered by the slicing contains no outer trapped surfaces. Thus, an important feature of the numerical collapse examples of Shapiro and Teukolsky, cited by them as evidence against cosmic censorship, does not appear to be qualitatively different from features which occur (for an appropriate choice of slicing) in the standard examples of collapse to a black hole.