Initial data and spherical dust collapse

Details Initial data and spherical dust collapse Initial data and spherical dust collapse

2000-02-17

arxiv.org/abs/gr-qc/0002062v1

Phys.Rev. D62 (2000) 044001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 1 figure, accepted for publication in Physical Review D

Scientific paper

10.1103/PhysRevD.62.044001

By considering families of radial null geodesics, we study the subsets of initial data that lead to naked singularities and black holes in inhomogeneous spherical dust collapse. We introduce the notion of central homogeneity for spherical dust collapse and prove that for the occurrence of naked singularities, the initial data set must in general be centrally homogeneous. Even though mathematically this indicates that naked singularities are in general unstable, we show that centrally inhomogeneous perturbations in the initial data are not physically reasonable. This provides an example of the fact that instability in this context deduced with respect to general perturbations can become stabilised once the class of perturbations are restricted to be physical.

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