Il Nuovo Cimento B (1971-1996)

, Volume 111, Issue 1, pp 39–48 | Cite as

Quasi-linear coordinates in general relativity

  • A. San Miguel
  • F. Vicente


An extension of the Jost and Karcher coordinates to the relativistic space-time is studied. The domain and Hessian of these extended coordinates are bounded by functions vanishing if the space-time is flat. The quasi-linearity property is analysed in the class of space-times obtained by Tzanakis which generalize the Robertson-Walker model. The transformation of normal Fermi coordinates into quasi-linear coordinates is obtained. Finally, the approximate position vector fields defined using Jost-Karcher coordinates and normal Fermi coordinates are compared.


04.20 General relativity 


02.40 Geometry, differential geometry, and topology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Jost J. andKarcher H.,Manuscr. Math.,40 (1982) 27.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    DeTurck D. M. andKazdan J. L.,Ann. Sci. Ecole Norm. Sup.,14 (1981) 249.MathSciNetMATHGoogle Scholar
  3. [3]
    Ni W.-T. andZimmermann M.,Phys. Rev. D,17 (1978) 1473.ADSCrossRefMATHGoogle Scholar
  4. [4]
    Ni W.-T.,Chin. J. Phys.,15 (1977) 51.MATHGoogle Scholar
  5. [5]
    Li W.-Q. andNi W.-T.,J. Math Phys.,20 (1979) 1925.ADSCrossRefGoogle Scholar
  6. [6]
    Ruse H. S.,Proc. London Math. Soc.,32 (1931) 87.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Synge J. L.,Proc. London Math. Soc.,32 (1931) 241.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Synge J. L.,Relativity: the General Theory (North-Holland, Amsterdam) 1960.Google Scholar
  9. [9]
    DeWitt B. S. andBrehme R. W.,Ann. Phys. (N.Y.),9 (1960) 220.MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    Dixon W. G.,Gen. Relativ. Gravit.,4 (1973) 199.ADSCrossRefGoogle Scholar
  11. [11]
    Berger M.,Astérisque, Soc. Math. France,9 (1985) 9.MATHGoogle Scholar
  12. [12]
    Beem J. K. andParker P. E.,Comm. Math. Helv.,59 (1984) 319.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    Beem J. K. andParker P. E.,J. Math. Phys.,31 (1990) 819.MathSciNetADSCrossRefMATHGoogle Scholar
  14. [14]
    Kulkarini R. S.,Comm. Math. Helv.,54 (1979) 173.CrossRefGoogle Scholar
  15. [15]
    O'Neill B.,Semi-Riemannian Geometry (Academic Press, Orlando) 1983.MATHGoogle Scholar
  16. [16]
    Kaul H.,Manuscr. Math.,19 (1976) 261.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Tzanakis C.,Class. Quantum Grav.,8 (1991) 1913.MathSciNetADSCrossRefMATHGoogle Scholar
  18. [18]
    Schattner R. andTrümper M.,J. Phys. A,14 (1981) 2345.MathSciNetADSCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1996

Authors and Affiliations

  • A. San Miguel
    • 1
  • F. Vicente
    • 1
  1. 1.Departamento de Matemática Aplicada FundamentalUniversidad de ValladolidValladolidSpain

Personalised recommendations