 
Summary: arXiv:1007.4997v1[grqc]28Jul2010
INTERPRETING SOLUTIONS WITH NONTRIVIAL
KILLING GROUPS IN GENERAL RELATIVITY
SALVATORE ANTOCI AND DIERCKEKKEHARD LIEBSCHER
Abstract. General relativity is reconsidered by starting from the un
questionable interpretation of special relativity, which (Klein 1910) is
the theory of the invariants of the metric under the PoincarŽe 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 spe
cial 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 PoincarŽe "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 exam
