  When, at the end of the year 1915, both Einstein and Hilbert arrived at what
were named the field equations of general relativity, both of them thought that
their fundamental achievement entailed, inter alia, the realisation of a theory
of gravitation whose underlying group was the group of general coordinate
transformations. This group theoretical property was believed by Einstein to be
a relevant one from a physical standpoint, because the general coordinates
allowed to introduce reference frames not limited to the inertial reference
frames that can be associated with the Minkowski coordinate systems, whose
transformation group was perceived to be restricted to the Poincar\'e group.
Two years later, however, Kretschmann published a paper in which the physical
relevance of the group theoretical achievement in the general relativity of
1915 was denied. For Kretschmann, since any theory, whatever its physical
content, can be rewritten in a generally covariant form, the group of general
coordinate transformations is physically irrelevant. This is not the case,
however, for the group of the infinitesimal motions that bring the metric field
in itself, namely, for the Killing group. This group is physically
characteristic of any given spacetime theory, since it accounts for the local
invariance properties of the considered manifold, i.e., for its ``relativity
postulate''. In the present chapter it is shown what are the consequences for
the physical interpretation of some of these solutions whose relativity
postulate is of intermediate content, when Kretschmann's standpoint is
consistently adhered to.
