Advertisement

Relativistic Gravitational Fields with Close Newtonian Analogs

  • Pawel Nurowski
  • Engelbert Schucking
  • Andrzej Trautman

Abstract

Given a Newtonian velocity field v(x, t), one considers the manifold R 4 with the Lorentz metric g = (dx - v dt)2 - dt2. The Riemann tensor is computed and used to characterize flat space-times with g of this form. Among nonflat solutions of Einstein’s equations for such a g there are some cosmological models, the Schwarzschild and Kasner metrics and their generalizations to include matter fields and the cosmological constant. If ∣v∣=1, then the vector field ∂/∂t is null and has vanishing divergence; it is geodetic and shear-free if and only if v /∂t is parallel to v.

Keywords

Velocity Field Cosmological Constant Einstein Equation Perfect Fluid Null Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Heckmann, O. H. L. and Schucking, E. In Encycl. of Physics LIII 489 (Springer, Berlin, 1959).Google Scholar
  2. [2]
    Infeld, L. and Plebatiski, J. Motion and Relativity (PWN, Warszawa, 1960).MATHGoogle Scholar
  3. [3]
    Julia, B. and Nicolai, H. “Null-Killing vector dimensional reduction and Galilean geometrodynamics,” Preprint, LPTENS 94/21 and DESY (1994). 94–156.Google Scholar
  4. [4]
    Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. Exact Solutions of Einstein’s Equations (VEB Deutscher Verlag der Wiss., Berlin, 1980).MATHGoogle Scholar
  5. [5]
    Landau, L. D. and Lifshitz, E. M. The Classical Theory of Fields, Fourth Revised English Edition (Pergamon Press, Oxford, 1975).Google Scholar
  6. [6]
    Robinson, I. and Trautman, A. In Proc. of the Fourth Marcel Grossmann Meeting on General Relativity, R. Ruffini, ed. (Elsevier Science Publ., 1986).Google Scholar
  7. [7]
    Trautman, A. In Perspectives in Geometry and Relativity, B. Hoffmann, ed. (Indiana University Press, Bloomington, 1966).Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Pawel Nurowski
  • Engelbert Schucking
  • Andrzej Trautman

There are no affiliations available

Personalised recommendations