Relativistic Gravitational Fields with Close Newtonian Analogs
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.
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