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The Schwarzschild metric and the Friedmann equations from Newtonian Gravitational collapse

  • Guendelman, Eduardo I.
  • Banik, Arka Prabha
  • Granit, Gilad
  • Ygael, Tomer
  • Rohrhofer, Christian
Publication Date
May 29, 2015
Submission Date
Mar 30, 2015
arXiv ID: 1503.08803
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As is well known, the 0 - 0 component of the Schwarzschild space can be obtained by the requirement that the geodesic of slowly moving particles match the Newtonian equation. Given this result, we show here that the remaining components can be obtained by requiring that the inside of a Newtonian ball of dust matched at a free falling radius with the external space determines that space to be Schwarzschild, if no pathologies exist. Also we are able to determine that the constant of integration that appears in the Newtonian Cosmology, coincides with the spatial curvature of the FLRW metric. These results are of interest at least in two respects, one from the point of view of its pedagogical value of teaching General Relativity without in fact using Einstein's equation and second, the fact that some results attributed to General Relativity can be obtained without using General Relativity indicates that these results are more general than the particular dynamics specified by General Relativity.

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