Geometry and topology of singularities in spherical dust collapse

Abstract

We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if and only if there are future-pointing radial null geodesics emerging from the singularity. (ii) Limits of various space-time invariants and other useful quantities (relating to Thorne's point-cigar-barrel-pancake classification and to isotropy/entropy measures) are studied in the approach to the singularity. (iii) The topology of the singularity is studied from the point of view of ideal boundary structure. In each case, the different nature of the visible and censored region of the singularity is emphasized.

12 pages. To appear in Classical and Quantum Gravity

References in corpus (5)

• Singularity Theorems and Their Consequences
• Non-radial null geodesics in spherical dust collapse
• Appearance of the central singularity in spherical collapse
• Generalised hyperbolicity: hypersurface singularities
• Comment on ``Strength and genericity of singularities in Tolman-Bondi-de Sitter collapse'' and a note on central singularities

Cited by in corpus (13)

• Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
• Effects of Gauss-Bonnet term on the final fate of gravitational collapse
• Shadow of a naked singularity
• Effects of Lovelock terms on the final fate of gravitational collapse: analysis in dimensionally continued gravity
• Spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet Gravity
• How Does Naked Singularity Look?
• Global visibility of naked singularities
• Naked Singularities in Higher Dimensional Szekeres Space-time
• Spherically symmetric gravitational collapse of a dust cloud in third order Lovelock Gravity
• Relativistic Gravitational Collapse of a Cylindrical Shell of Dust
• Spherically symmetric perfect fluid in area-radial coordinates
• Gauge invariant perturbations of self-similar Lemaître-Tolman-Bondi spacetime: even parity modes with $l\ge 2$
• On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse