The case for the utility of Kruskal–Szekeres coordinates in the classroom made by Augousti et al in
this journal (2012 Eur. J. Phys. 33 [http://https://doi.org/10.1088/0143-0807/33/1/001] 1–11 ) 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 st…