Geodesic
On a~week solution of Einstein equations for expanding dust
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 43-49

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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 week 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.
Keywords: shell-crossing, inhomogeneous cosmology.
Mots-clés : Lemaitre–Tolman–Bondi solution 
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     title = {On a~week solution of {Einstein} equations for expanding dust},
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Sergey Ph. Tegai. On a~week solution of Einstein equations for expanding dust. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 43-49. http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a4/