# Interpreting solutions with nontrivial Killing groups in general relativity - General Relativity and Quantum Cosmology

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Abstract: General relativity is reconsidered by starting from the unquestionableinterpretation of special relativity, which Klein 1910 is the theory of theinvariants of the metric under the Poincar\-e group of collineations. Thisinvariance property is physical and different from coordinate properties.Coordinates are physically empty Kretschmann 1917 if not specified byphysics, and one shall look for physics again through the invariance group ofthe 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 generalsolution of the latter the invariance group is nil, and general relativitybehaves as an absolute theory, but when curvature vanishes the invariance groupis the group of infinitesimal Poincar\-e -Mitschleppen- of special relativity.Solutions of general relativity exist with invariance groups intermediatebetween the previously mentioned extremes. The Killing group properties of thestatic solutions of general relativity were investigated by Ehlers and Kundt1964. The particular case of Schwarzschild-s solution is examined, and theoriginal choice of the manifold done by Schwarzschild in 1916 is shown toderive invariantly from the uniqueness of the timelike, hypersurface orthogonalKilling vector of that solution.

Author: ** Salvatore Antoci, Dierck Ekkehard Liebscher**

Source: https://arxiv.org/