  We examine the causal and geometric horizons of dynamical black holes in
Lemaitre-Tolman-Bondi collapsing dust spacetimes. Marginally trapped tubes in
these spacetimes may be spacelike, timelike or null and may also be sourced
from or disappear into shell-crossing singularities which we resolve with
(timelike) shockwaves. The event horizon kinks when it intersects a shockwave.
We calculate the timelike separation between the crossable boundary (marginally
trapped tubes plus connecting shockwaves) and event horizon. As measured along
the crossable boundary this function can have discontinuities not only in its
derivative but also in the function itself. These features are closely related
to the geometry of the crossable boundary. Finally, we consider the application
of this work for future space explorers seeking to make a closest
(non-terminal) approach to a black hole horizon.
