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Is the shell-focusing singularity of Szekeres space-time visible?

Nolan, Brien C. and Debnath, Ujjal (2007) Is the shell-focusing singularity of Szekeres space-time visible? Physical Review D, 76 (10). 104046-1-104046-10. ISSN 1550-7998

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Abstract

The visibility of the shell-focusing singularity in Szekeres space-time—which represents quasispherical dust collapse—has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaître-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:general relativity; quantum cosmology;
Subjects:Mathematics
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:The American Physical Society
Official URL:http://dx.doi.org/10.1103/PhysRevD.76.104046
Copyright Information:© 2007 The American Physical Society
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:15642
Deposited On:10 Aug 2010 10:18 by DORAS Administrator. Last Modified 10 Aug 2010 10:18

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