On a weak solution of Einstein equations for expanding dust

Details On a weak solution of Einstein equations for expanding dust On a weak solution of Einstein equations for expanding dust

2011-04-09

arxiv.org/abs/1104.1664v1

Journal of Siberian Federal University. Mathematics & Physics 2011, 4(1), 43-49

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, 3 figures

Scientific paper

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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