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

Abstract

The visibility of the shell-focusing singularity in Szekeres space-time - which represents quasi-spherical 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 non-parallel radial geodesic, then the space-time is spherically symmetric, and so is a Lema\^ıtre-Tolman-Bondi (LTB) 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 non-radial null geodesics in the axially symmetric case and in the general (non-axially symmetric) case, and suggest a possible approach.

10 pages

References in corpus (9)

• Naked strong curvature singularities in Szekeres space-times
• Non-radial null geodesics in spherical dust collapse
• On the global visibility of singularity in quasi-spherical collapse
• Quasi-Spherical Gravitational Collapse in Any Dimension
• Strong curvature singularities in quasispherical asymptotically de Sitter dust collapse
• Naked Singularities in Higher Dimensional Szekeres Space-time
• Sufficient condition for Blackhole formation in spherical gravitational collapse
• Quasi-spherical gravitational collapse and the role of initial data, anisotropy and inhomogeneity
• Role of Initial Data in Higher Dimensional Quasi-Spherical Gravitational Collapse

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