### Abstract

In spherical symmetry, the total energy-momentum tensor near the apparent horizon is identified up to a single function of time from two assumptions: a trapped region forms at a finite time of a distant observer, and values of two curvature scalars are finite at its boundary. In general relativity, this energy-momentum tensor leads to the unique limiting form of the metric. The null energy condition is violated across the apparent horizon and is satisfied in the vicinity of the inner apparent horizon. As a result, homogenous collapse models cannot describe the formation of a black hole. Properties of matter change discontinuously immediately after formation of a trapped region. Absolute values of comoving density, pressure, and flux coincide at the apparent horizon. Thus, collapse of ideal fluids cannot lead to the formation of black holes. Moreover, these three quantities diverge at the expanding apparent horizon, producing a regular (i.e., finite curvature) firewall. This firewall is incompatible with quantum energy inequalities, implying that trapped regions, once formed at some finite time of a distant observer, cannot grow.

Original language | English |
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Article number | 124025 |

Pages (from-to) | 124025-1-124025-8 |

Number of pages | 8 |

Journal | Physical Review D |

Volume | 100 |

Issue number | 12 |

DOIs | |

Publication status | Published - 15 Dec 2019 |

### Bibliographical note

Copyright 2019 American Physical Society. Firstly published in Physical Review D, 100(12), 124025. The original publication is available at https://doi.org/10.1103/PhysRevD.100.124025. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.### Cite this

*Physical Review D*,

*100*(12), 124025-1-124025-8. [124025]. https://doi.org/10.1103/PhysRevD.100.124025