  This is a companion article to `Using massless fields for observing black
hole features in the collapsed phase of Euclidean dynamical triangulations'
[1]. It clarifies a singular co\"{o}rdinate transformation of an $SO(4)$
invariant metric to the usual spherical co\"{o}rdinates in which, at an instant
of time called zero, the metric takes the form of a black hole with an
interior. Regular transformations are also studied and found to lead in the
zero time limit to the same spatial components of the metric as with the
singular one, whereas the time component ends up differently. Components of the
Einstein tensor also end up the same. A regular black hole metric is inversely
transformed and compared with simulation results in [1].
