 
Summary: arXiv:0910.2073v1[grqc]12Oct2009
THE GROUP ASPECT IN THE PHYSICAL
INTERPRETATION OF GENERAL RELATIVITY THEORY
SALVATORE ANTOCI AND DIERCKEKKEHARD LIEBSCHER
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 gravita
tion 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 refer
ence 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 PoincarŽe 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,
