Nurowski, Pawel; Schucking, Engelbert; Trautman, Andrzej Relativistic gravitational fields with close Newtonian analogs. (English) Zbl 0977.53515 Harvey, Alex (ed.), On Einstein’s path: essays in honor of Engelbert Schücking. A symposium, New York Univ., New York, NY, USA, December 12-13, 1996. New York, NY: Springer. 329-337 (1999). Summary: Given a Newtonian velocity field \({\mathbf v}({\mathbf x}, t)\), one considers the manifold \(\mathbb{R}^4\) with the Lorentz metric \(g=(d{\mathbf x}- {\mathbf v} d t)^2-dt^2\). 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 \(|{\mathbf v}|=1\), then the vector field \(\partial/ \partial t\) is null and has vanishing divergence; it is geodetic and shear-free if and only if \(\partial {\mathbf v}/\partial t\) is parallel to \({\mathbf v}\).For the entire collection see [Zbl 0913.00041]. Cited in 1 Document MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory 53C80 Applications of global differential geometry to the sciences Keywords:Schwarzschild metric; Newtonian velocity field; flat space-times; Einstein’s equations; cosmological models; Kasner metrics PDFBibTeX XMLCite \textit{P. Nurowski} et al., in: On Einstein's path: essays in honor of Engelbert Schucking. A symposium, New York Univ., New York, NY, USA, December 12--13, 1996. New York, NY: Springer. 329--337 (1999; Zbl 0977.53515)