Skip to main content
SpringerLink
Log in

Induced volume forms with applications in relativistic kinetic theory

  • Research Articles
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Covariant volume forms are defined in an intrinsic way on a general submanifold of aC ∞ manifold carrying a nondegenerate metric of unspecified signature. The case of covariant volume forms induced on hypersurfaces, null and nonnull, is examined in detail. The results obtained are applied to the various submanifolds of the one-particle phase space of relativistic kinetic theory. Finally a proof of Liouville's theorem is given and its consequences on the Liouville vector are discussed.

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. Ehlers, J. (1971). General relativity and kinetic theory, inProceedings of the International School of Physics, “Enrico Fermi”Course 47, R. K. Sachs, ed. (Academic Press, New York).

    Google Scholar 

  2. Stewart, J. M. (1971). Non-equilibrium relativistic kinetic theory, inLecture Notes in Physics No. 10 (Springer-Verlag, Berlin).

    Google Scholar 

  3. Isreal, W. (1972). The relativistic Boltzman equation, inGeneral Relativity, L. O'Raifeartaigh, ed. (Oxford University Press, London).

    Google Scholar 

  4. Lindguist, R. (1966).Ann. Phys. (N.Y.),37, 487.

    Google Scholar 

  5. Marle, C. (1969).Ann. Inst. Henri Poincaré,10, 67.

    Google Scholar 

  6. Chernikov, N. A. (1962).Sov. Phys.-Dokl.,7, 397.

    Google Scholar 

  7. Chernokov, N. A. (1963).Acta Phys. Polonica,23, 629.

    Google Scholar 

  8. Yano, K., and Ishihara, S. (1973).Tangent and Cotangent Bundles (Marcel Dekker, New York).

    Google Scholar 

  9. Abraham, R., and Marsden, J. E. (1967).Foundations of Mechanics (Benjamin, New York).

    Google Scholar 

  10. Hawking, S., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge).

    Google Scholar 

  11. Synge, J. L. (1956).Relativity: The Special Theory (North-Holland, Amsterdam).

    Google Scholar 

  12. Sasaki, S. (1958).Tôhoku Math. J. 10, 338.

    Google Scholar 

  13. Sasaki, S. (1962).Tôhoku Math. J.,14, 146.

    Google Scholar 

  14. Jackson, J. D. (1963).1962 Brandeis Lectures Vol. I (Benjamin, New York).

    Google Scholar 

  15. Friedlander, F. G. (1975).The Wave Equation on a Curved Space-Time (Cambridge University Press, Cambridge).

    Google Scholar 

  16. Barrabes, C., and Henry, J. (1976).J. Phys. A: Math. Gen.,9, 1425.

    Google Scholar 

  17. Barrabes, C. (1982).Nuovo Cimento.,68B, 161.

    Google Scholar 

Download references

Author information

Author notes

  1. M. Tsamparlis

    Present address: Department of Physics, Division of Mechanics-Astronomy-Astrophysics, University of Athens, Athens GR 15771 Zografou, Greece

Authors and Affiliations

  1. Department of Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, 2001, J.H.B., South Africa

    M. Tsamparlis

Authors
  1. M. Tsamparlis
    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

Tsamparlis, M. Induced volume forms with applications in relativistic kinetic theory. Gen Relat Gravit 17, 831–851 (1985). https://doi.org/10.1007/BF00773681

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00773681

Keywords

Search

Navigation