  Marginally trapped surfaces (MTSs) are commonly used in numerical relativity
to locate black holes. For dynamical black holes, it is not known generally if
this procedure is sufficiently reliable. Even for Schwarzschild black holes,
Wald and Iyer constructed foliations which come arbitrarily close to the
singularity but do not contain any MTSs. In this paper, we review the Wald-Iyer
construction, discuss some implications for numerical relativity, and
generalize to the well known Vaidya spacetime describing spherically symmetric
collapse of null dust. In the Vaidya spacetime, we numerically locate
non-spherically symmetric trapped surfaces which extend outside the standard
spherically symmetric trapping horizon. This shows that MTSs are common in this
spacetime and that the event horizon is the most likely candidate for the
boundary of the trapped region.
