TY - JOUR

T1 - Schwarzschild and Friedmann Lemaître Robertson Walker metrics from Newtonian Gravitational collapse

AU - Guendelman, Eduardo I.

AU - Banik, Arka Prabha

AU - Granit, Gilad

AU - Ygael, Tomer

AU - Rohrhofer, Christian

PY - 2015

Y1 - 2015

N2 - 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 shall 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 pathology 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.

AB - 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 shall 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 pathology 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.

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JO - arxiv gr-qc

JF - arxiv gr-qc

ER -