  General relativity is reconsidered by starting from the unquestionable
interpretation of special relativity, which (Klein 1910) is the theory of the
invariants of the metric under the Poincar\'e group of collineations. This
invariance property is physical and different from coordinate properties.
Coordinates are physically empty (Kretschmann 1917) if not specified by
physics, and one shall look for physics again through the invariance group of
the metric. To find the invariance group for the metric, the Lie "Mitschleppen"
is ideal for this task both in special and in general relativity. For a general
solution of the latter the invariance group is nil, and general relativity
behaves as an absolute theory, but when curvature vanishes the invariance group
is the group of infinitesimal Poincar\'e "Mitschleppen" of special relativity.
Solutions of general relativity exist with invariance groups intermediate
between the previously mentioned extremes. The Killing group properties of the
static solutions of general relativity were investigated by Ehlers and Kundt
(1964). The particular case of Schwarzschild's solution is examined, and the
original choice of the manifold done by Schwarzschild in 1916 is shown to
derive invariantly from the uniqueness of the timelike, hypersurface orthogonal
Killing vector of that solution.
