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

P. S. Joshi·T. P. Singh
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Abstract

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 $ρ_{c}$, 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 $β$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $β$ 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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P. S. Joshi, T. P. Singh. 1995-03-15. On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust. https://doi.org/10.1103/physrevd.51.6778

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