On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

Details On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

1994-05-17

arxiv.org/abs/gr-qc/9405036v2

Phys.Rev. D51 (1995) 6778-6782

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Original title changed, numerical range of naked singularity corrected. Plain Tex File. 14 pages. To appear in Physical Review

Scientific paper

10.1103/PhysRevD.51.6778

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.

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