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

Why ghosts don't touch: a tale of two adventurers falling one after another into a black hole