The Parametric Manifold Picture of Space-Time

  • Zoltán Perjés
Part of the NATO ASI Series book series (NSSB, volume 245)


Parametric manifolds are reparametrization-invariant geometric structures describing space-time and internal degrees of freedom in a unified framework. Using the theory of parametric spinors, a decomposition of the space-time in General Relativity is developed with respect to the 3-space of trajectories of a time-like or space-like vector field. The parametric 3+1 decomposition surpasses the ADM formalism in generality since it is possible even in space-times which do not admit a space-like foliation.


Soldering Form Covariant Derivative Bianchi Identity Spinor Index Parametric Spinor 
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  1. [1]
    Arnowitt, R., Deser, S. and Misner, C. W., in Gravitation, Ed. Witten, L. (Wiley, 1962)Google Scholar
  2. [2]
    Gödel, K., Rev. Mod. Phys. 21, 447 (1949)ADSzbMATHCrossRefGoogle Scholar
  3. [3]
    Ehlers, J., in: Les théories relativistes de ¡a gravitation (CNRS, Paris, 1959)Google Scholar
  4. [4]
    Schouten, J. A.: Ricci-calculus (Springer, Berlin, 1954)zbMATHCrossRefGoogle Scholar
  5. [5]
    Stachel, J.: Congruences of subspaces, in: Gravitation and Geometry, Eds. Rindler, W. and Trautman, A. (Bibliopolis, 1987)Google Scholar
  6. [6]
    Lottermoser, M.: Über den Newtonschen Grenzwert der Allgemeinen Relativitätstheorie und die relativistische Erweiterung Newtonscher Anfangsdaten (Dissertation, Munich, 1988)Google Scholar
  7. [7]
    Zelmanov, A. L.: K relativistskoj teorii anizotropnoj nieodnorodnoj vselennoj, in: Trudi shestovo soveshanija po voprosam kosmologii, p. 144, Acad. Publ. USSR, 1959,Google Scholar
  8. [8]
    Zelmanov, A. L., Dokl. Akad. USSR 107, 815 (1956)MathSciNetGoogle Scholar
  9. [9a]
    Perjés, Z., Int. J. Theor. Phys. 10, 217 (1974),CrossRefGoogle Scholar
  10. [9b]
    Perjés, Z., Commun. Math. Phys. 12, 275 (1969)ADSCrossRefGoogle Scholar
  11. [10]
    Perjés, Z., J. Math. Phys. 11, 3383 (1970)ADSCrossRefGoogle Scholar
  12. [11]
    Penrose, R.: Structure of space-time, in: Batteile Rencontres, Eds. DeWitt, C. M. and Wheeler, J. A. (Benjamin, 1968)Google Scholar
  13. [12]
    Carter, B. and Quintana, H., Proc. Roy. Soc. 331, 57 (1972)MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. [13]
    Ernst, F. J., Phys. Rev. 167, 1175 (1968)ADSCrossRefGoogle Scholar
  15. [14]
    Pirani, F. A. E., in: Lectures in General Relativity Brandeis Summer Institute in Theoretical Physics (Prentice-Hall, Englewood Cliffs, N. J. 1964)Google Scholar
  16. [15]
    Perjés, Z., unpublished (1971)Google Scholar
  17. [16]
    Sen, A., J. Math. Phys. 22, 1718 (1981)Google Scholar
  18. [17]
    Isham, C., in: Quantum Gravity, Eds. Isham, C., Penrose, R. and Sciama, D., Oxford University Press, 1984Google Scholar
  19. [18]
    Ashtekar, A., Phys. Rev. D36, 1587 (1987)MathSciNetADSGoogle Scholar
  20. [19]
    Perjés, Z., Dissertation, Magyar Fizikai Folyóirat XXIV, 173 (1976)Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Zoltán Perjés
    • 1
  1. 1.Central Research Institute for PhysicsBudapest 114Hungary

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