  According to the Einstein hole argument, vacuum metric solutions are
equivalent only if they correspond to the same energy--momentum tensor in the
source region. In this paper it is shown that singular coordinates that are
used to show Schwarzschild geodesics completeness, introduce the fictive
delta-like sources at the horizon. Then, metric tensors obtained by such
singular transformations, cannot be considered as solutions of the same
Einstein equations with the central source.
