  The case for the utility of Kruskal-Szekeres coordinates in classroom made by
Augousti et al. in this journal (Eur. J. Phys. 33:1--11, 2012) is strengthened
by extending their discussion beyond the event horizon of the black hole.
Observations made by two adventurers following one another into a Schwarzschild
black hole are examined in terms of these nonsingular coordinates. Two
scenarios are considered, the first corresponding to one observer following the
other closely, the second to a significant distance between the two of them,
precluding the existence of a common inertial system. In particular, the
concepts of distance and temporal separation near the horizon and the redshift
of the first infaller's image as seen by the second are investigated. The
results show that the notion of "touching ghosts" does not correspond to the
local physics of two observers falling into a black hole. The story line is
interesting enough and the mathematical details are sufficiently simple to use
the example in a general relativity course, even at the undergraduate level.
