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arXiv · 1104.1664

On a weak solution of Einstein equations for expanding dust

Sergey Ph. Tegai
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Abstract

An expanding spherically symmetric dust cloud is considered in a framework of general relativity. Initial conditions leading to a shell-crossing singularity are chosen. The way to construct a weak solution for such a case is proposed. Suggested method consists in cutting off the region containing the shell-crossing and matching the remaining parts of space-time at a thin shell. Junction conditions determine the motion of that thin shell. The singular part of dust stress-energy tensor is nontrivial only after the shell-crossing occurs. Before that the solution coincides with Lemaitre - Tolman - Bondi one. A toy model representing an underdensed region in Universe is discussed.

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Sergey Ph. Tegai. 2011-04-09. On a weak solution of Einstein equations for expanding dust. https://doi.org/10.1142/9789814374552_0224

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