Energy-momentum tensor and metric near the Schwarzschild sphere

Valentina Baccetti, Robert B. Mann, Sebastian Murk, Daniel Terno

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    15 Citations (Scopus)
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    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 languageEnglish
    Article number124014
    Number of pages11
    JournalPhysical Review D: covering particles, fields, gravitation, and cosmology
    Issue number12
    Publication statusPublished - 11 Jun 2019

    Bibliographical note

    Copyright 2019 American Physical Society. Firstly published in Physical Review D, 99(12), 124014. The original publication is available at 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.


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