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

Dust Manifold 

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Pawel Nurowski
  • Engelbert Schucking
  • Andrzej Trautman

There are no affiliations available

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