Abstract
We review the solution to the equivalence problem in general relativity given by Cartan and Brans and present a practically useful method to obtain a coordinate-invariant description of a geometry. The method, which can be seen as a generalized Petrov classification, automatically gives the dimensions of the isometry group and its isotropy subgroup. Finally, we illustrate the method using the Schwarzschild solution as a very simple example.
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Karlhede, A. A review of the geometrical equivalence of metrics in general relativity. Gen Relat Gravit 12, 693–707 (1980). https://doi.org/10.1007/BF00771861
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DOI: https://doi.org/10.1007/BF00771861