This article is cited 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.

UDC: 530.12+524.8

Received: 04.06.2010
Received in revised form: 17.07.2010
Accepted: 20.09.2010

Language: English