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Il Nuovo Cimento (1955-1965)

, Volume 18, Supplement 1, pp 36–47 | Cite as

Invariants of general relativity

II. — Classification of spaces
  • A. Peres
Article

Summary

Petrov’s classification of pure gravitational fields is generalized to the case where matter is present. It is shown how the Petrov invariants can be computed directly,i.e. without the intermediate stage of quasi-Galilean coordinates (or tetrads, or spinors) that was required in previous works. It is further shown that if some of the invariants of Géhéniau and Debever vanish, it is sometimes possible to find new algebraic invariants of the Riemann tensor, which are independent of those of Géhéniau and Debever. This fact is especially interesting when all the Géhéniau-Debever invariants vanish, as is shown by an example.

Riassunto

Si generalizza la classificazione di Petrov dei puri campi gravitazionali al caso in cui si ha presenza di materia. Si mostra come gli invarianti di Petrov si possano calcolare direttamente, cioè senza lo stadio intermedio delle coordinate (o tetradi, o spinori) quasi-Galileane, che era richiesto nel lavoro precedente. Si mostra inoltre che se alcuni degli invarianti di Géhéniau e Debever si annullano, è possibile talvolta trovare nuovi invarianti algebrici del tensore di Riemann, che sono indipendenti dagli invarianti di Géhéniau e Debever. Questo fatto è molto interessante nel caso in cui tutti gli invarianti di Géhéniau e Debever si annullano, come si mostra con un esempio.

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Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • A. Peres
    • 1
  1. 1.Department of PhysicsIsrael Institute of TechnologyHaifa

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