A review of the geometrical equivalence of metrics in general relativity
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.
- Publication:
-
General Relativity and Gravitation
- Pub Date:
- September 1980
- DOI:
- 10.1007/BF00771861
- Bibcode:
- 1980GReGr..12..693K