Genericity of black holes and naked singularities in gravitational collapse

Details Genericity of black holes and naked singularities in gravitational collapse Genericity of black holes and naked singularities in gravitational collapse

2011-07-19

arxiv.org/abs/1107.3749v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

38 pages, 3 figures

Scientific paper

We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. Our aim is to examine and characterize the above two possible outcomes in terms of stability of the initial data and genericity. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, once genericity is defined in a suitable sense in an appropriate space. The occurrence of naked singularities in collapse is examined in terms of the initial data and the allowed evolutions to show that naked singularities arise generically under suitable physical conditions and as evolving from a regular initial data.

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