### Abstract

Within the Lemaître-Tolman-Bondi formalism for the gravitational collapse of inhomogeneous dust, we analyze the parameter space that leads to the formation of a globally covered singularity (i.e. a black hole) when some physically reasonable requirements are imposed (namely, a positive, radially decreasing and quadratic profile for the energy density and the avoidance of shell crossing singularities). It turns out that a black hole can occur as the endstate of collapse only if the singularity is simultaneous, as in the standard Oppenheimer-Snyder scenario. Given a fixed density profile, there is one velocity profile for the infalling particles that will produce a black hole. All other allowed velocity profiles will terminate the collapse in a locally naked singularity.

Original language | English |
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Article number | 145004 |

Journal | Classical and Quantum Gravity |

Volume | 32 |

Issue number | 14 |

DOIs | |

Publication status | Published - Jul 23 2015 |

### Keywords

- black holes
- gravitational collapse
- naked singularities

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*Classical and Quantum Gravity*,

*32*(14), [145004]. https://doi.org/10.1088/0264-9381/32/14/145004