### Abstract

Regularity of the horizon radius rg of a collapsing body constrains a limiting form of a spherically symmetric energy-momentum tensor near it. Its nonzero limit belongs to one of four classes that are distinguished only by two signs. As a result, close to rg the geometry can always be described by either an ingoing or outgoing Vaidya metric with increasing or decreasing mass. If according to a distant outside observer the trapped regions form in finite time, then the Einstein equations imply violation of the null energy condition. In this case the horizon radius and its rate of change determine the metric in its vicinity, and the hypersurface r=rg(t) is timelike during both the expansion and contraction of the trapped region. We present the implications of these results for the firewall paradox and discuss arguments that the required violation of the null energy condition is incompatible with the standard analysis of black hole evaporation.

Original language | English |
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Article number | 124014 |

Number of pages | 11 |

Journal | Physical Review D |

Volume | 99 |

Issue number | 12 |

DOIs | |

Publication status | Published - 11 Jun 2019 |

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## Cite this

Baccetti, V., Mann, R. B., Murk, S., & Terno, D. (2019). Energy-momentum tensor and metric near the Schwarzschild sphere.

*Physical Review D*,*99*(12), [124014]. https://doi.org/10.1103/PhysRevD.99.124014