General Relativity and Gravitation

, Volume 12, Issue 9, pp 693–707 | Cite as

A review of the geometrical equivalence of metrics in general relativity

  • A. Karlhede
Research Articles


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.


General Relativity Isotropy Differential Geometry Isometry Group Equivalence Problem 
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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • A. Karlhede
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of StockholmStockholmSweden

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