## Abstract

We consider spherically-symmetric black holes in semiclassical gravity. For a collapsing radiating thin shell we derive a sufficient condition on the exterior geometry that ensures that a black hole is not formed. This is also a sufficient condition for an infalling test particle to avoid the apparent horizon of an existing black hole and approach it only within a certain minimal distance. Taking the presence of a trapped region and its outer boundary - the apparent horizon- as the defining feature of black holes, we explore the consequences of their finite time of formation according to a distant observer. Assuming regularity of the apparent horizon we obtain the limiting form of the metric and the energy-momentum tensor in its vicinity that violates the null energy condition (NEC). The metric does not satisfy the sufficient condition for horizon avoidance: a thin shell collapses to form a black hole and test particles (unless too slow) cross into it in finite time. However, there may be difficulty in maintaining the expected range of the NEC violation, and stability against perturbations is not assured.

Original language | English |
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Title of host publication | MG15 |

Subtitle of host publication | Proceedings of the Fifteenth Marcel Grossman Meeting on General Relativity |

Editors | Elia Battistelli, Robert T. Jantzen, Remo Ruffini |

Publication status | E-pub ahead of print - 2022 |

Event | 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, MG 2018 - Rome, Italy Duration: 1 Jul 2018 → 7 Jul 2018 |

### Conference

Conference | 15th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, MG 2018 |
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Country/Territory | Italy |

City | Rome |

Period | 1/07/18 → 7/07/18 |

## Keywords

- Black holes
- Null energy condition
- Thin shells