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General relativity without coordinates

  • Published:
Il Nuovo Cimento (1955-1965)

Summary

In this paper we develop an approach to the theory of Riemannian manifolds which avoids the use of co-ordinates. Curved spaces are approximated by higher-dimensional analogs of polyhedra. Among the advantages of this procedure we may list the possibility of condensing into a simplified model the essential features of topologies like Wheeler’s wormhole and a deeper geometrical insight.

Riassunto

In questo lavoro viene sviluppato il formalismo matematico della relatività generalizzata in modo da evitare l’uso di coordinate. A tal uopo si introducono decomposizioni simpliciali di varietà rimanniane che costituiscono l’analogo iperdimensionale di poliedri. Si spera che questo nuovo formalismo renda possibile la discussione di soluzioni delle equazioni di Einstein corrispondenti a topologie di elevata complessità.

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Literatur

  1. P. S. Aleksandrov:Topologia combinatoria (Torino, 1957).

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Additional information

Nov at the University, Torino.

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Cite this article

Regge, T. General relativity without coordinates. Nuovo Cim 19, 558–571 (1961). https://doi.org/10.1007/BF02733251

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  • DOI: https://doi.org/10.1007/BF02733251

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