Skip to main content
SpringerLink
Log in

Quasi-linear coordinates in general relativity

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Jost J. andKarcher H.,Manuscr. Math.,40 (1982) 27.

    Article  MathSciNet  MATH  Google Scholar 

  2. DeTurck D. M. andKazdan J. L.,Ann. Sci. Ecole Norm. Sup.,14 (1981) 249.

    MathSciNet  MATH  Google Scholar 

  3. Ni W.-T. andZimmermann M.,Phys. Rev. D,17 (1978) 1473.

    Article  ADS  MATH  Google Scholar 

  4. Ni W.-T.,Chin. J. Phys.,15 (1977) 51.

    MATH  Google Scholar 

  5. Li W.-Q. andNi W.-T.,J. Math Phys.,20 (1979) 1925.

    Article  ADS  Google Scholar 

  6. Ruse H. S.,Proc. London Math. Soc.,32 (1931) 87.

    Article  MathSciNet  Google Scholar 

  7. Synge J. L.,Proc. London Math. Soc.,32 (1931) 241.

    Article  MathSciNet  Google Scholar 

  8. Synge J. L.,Relativity: the General Theory (North-Holland, Amsterdam) 1960.

    Google Scholar 

  9. DeWitt B. S. andBrehme R. W.,Ann. Phys. (N.Y.),9 (1960) 220.

    Article  MathSciNet  ADS  Google Scholar 

  10. Dixon W. G.,Gen. Relativ. Gravit.,4 (1973) 199.

    Article  ADS  Google Scholar 

  11. Berger M.,Astérisque, Soc. Math. France,9 (1985) 9.

    MATH  Google Scholar 

  12. Beem J. K. andParker P. E.,Comm. Math. Helv.,59 (1984) 319.

    Article  MathSciNet  MATH  Google Scholar 

  13. Beem J. K. andParker P. E.,J. Math. Phys.,31 (1990) 819.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Kulkarini R. S.,Comm. Math. Helv.,54 (1979) 173.

    Article  Google Scholar 

  15. O'Neill B.,Semi-Riemannian Geometry (Academic Press, Orlando) 1983.

    MATH  Google Scholar 

  16. Kaul H.,Manuscr. Math.,19 (1976) 261.

    Article  MathSciNet  Google Scholar 

  17. Tzanakis C.,Class. Quantum Grav.,8 (1991) 1913.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Schattner R. andTrümper M.,J. Phys. A,14 (1981) 2345.

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada Fundamental, Universidad de Valladolid, Valladolid, Spain

    A. San Miguel & F. Vicente

Authors
  1. A. San Miguel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Vicente
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miguel, A.S., Vicente, F. Quasi-linear coordinates in general relativity. Nuov Cim B 111, 39–48 (1996). https://doi.org/10.1007/BF02726199

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02726199

PACS

PACS

Search

Navigation