Geometry and topology of singularities in spherical dust collapse

TL;DR

This paper investigates the geometric and topological properties of singularities in inhomogeneous dust collapse, analyzing geodesics, invariants, and boundary structures to understand their nature and visibility.

Contribution

It provides new insights into the conditions for geodesic emergence, invariant limits, and the topology of singularities in spherical dust collapse.

Findings

Radial and non-radial timelike geodesics emerge simultaneously from the singularity.

Limits of spacetime invariants are characterized near the singularity.

The topology of the singularity's boundary structure is analyzed.

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.