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Singularities and asymptotic behavior of the Tolman-Bondi model

Alexander Gromov
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Abstract

The Bondi formula for calculation of the invariant mass in the Tolman- Bondi (TB) model is interprated as a transformation rule on the set of co-moving coordinates. The general procedure by which the three arbitrary functions of the TB model are determined explicitly is presented. The properties of the TB model, produced by the transformation rule are studied. Two applications are studied: for the falling TB flat model the equation of motion of two singularities hypersurfaces are obtained; for the expanding TB flat model the dependence of size of area with friedmann-like solution on initial conditions is studied in the limit $t \to +\infty$.

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Alexander Gromov. 1997-06-04. Singularities and asymptotic behavior of the Tolman-Bondi model. https://arxiv.org/abs/gr-qc/9706013

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