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J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 1, Pages 43–49 (Mi jsfu160)  

This article is cited in 1 scientific paper (total in 1 paper)

On a week solution of Einstein equations for expanding dust

Sergey Ph. Tegai

Institute of Engineering Physics & Radio-Electronics, Siberian Federal University, Krasnoyarsk, Russia

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 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, Lemaitre–Tolman–Bondi solution, inhomogeneous cosmology.

Full text: PDF file (144 kB)
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UDC: 530.12+524.8
Received: 04.06.2010
Received in revised form: 17.07.2010
Accepted: 20.09.2010
Language:

Citation: Sergey Ph. Tegai, “On a week solution of Einstein equations for expanding dust”, J. Sib. Fed. Univ. Math. Phys., 4:1 (2011), 43–49

Citation in format AMSBIB
\Bibitem{Teg11}
\by Sergey~Ph.~Tegai
\paper On a~week solution of Einstein equations for expanding dust
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 1
\pages 43--49
\mathnet{http://mi.mathnet.ru/jsfu160}


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    This publication is cited in the following articles:
    1. Tippett B.K., Booth I., “Closest Safe Approach To An Accreting Black Hole”, Phys. Rev. D, 90:8 (2014), 084027  crossref  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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