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arXiv · 1912.12863

Distance between collapsing matter and trapping horizon in evaporating black holes

Pei-Ming Ho·Yoshinori Matsuo·Yuki Yokokura
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Abstract

Assuming that the vacuum energy-momentum tensor is not exceptionally large, we consider 4D evaporating black holes with spherical symmetry and evaluate the proper distance $\Delta L$ between the time-like apparent horizon and the surface of the collapsing matter after it has entered the apparent horizon. We show that $\Delta L$ can never be larger than $\mathcal{O}(n^{3/2}\ell_p)$ when the black hole is evaporated to $1/n$ of its initial mass, as long as $n \ll a^{2/3}/\ell_p^{2/3}$ (where $a$ is the Schwarzschild radius and $\ell_p$ is the Planck length). For example, the distance between the matter and the apparent horizon must be Planckian at the Page time.

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Pei-Ming Ho, Yoshinori Matsuo, Yuki Yokokura. 2019-12-30. Distance between collapsing matter and trapping horizon in evaporating black holes. https://doi.org/10.1103/physrevd.104.064005

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