Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-05-28
Phys.Rev.D76:124013,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30 pages, 21 figures; several corrections after referee's comments, 4 figures modified
Scientific paper
10.1103/PhysRevD.76.124013
In a previous paper we formulated a set of necessary conditions for the spherically symmetric weakly charged dust to avoid Big Bang/Big Crunch, shell crossing and permanent central singularities. However, we did not discuss the properties of the energy density, some of which are surprising and seem not to have been known up to now. A singularity of infinite energy density does exist -- it is a point singularity situated on the world line of the center of symmetry. The condition that no mass shell collapses to $R = 0$ if it had $R > 0$ initially thus turns out to be still insufficient for avoiding a singularity. Moreover, at the singularity the energy density $\epsilon$ is direction-dependent: $\epsilon \to - \infty$ when we approach the singular point along a $t =$ const hypersurface and $\epsilon \to + \infty$ when we approach that point along the center of symmetry. The appearance of negative-energy-density regions turns out to be inevitable. We discuss various aspects of this property of our configuration. We also show that a permanently pulsating configuration, with the period of pulsation independent of mass, is possible only if there exists a permanent central singularity.
Bolejko Krzysztof
Krasinski Andrzej
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