Distance between collapsing matter and trapping horizon in evaporating black holes

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.

16 pages

References in corpus (8)

• A Primer for Black Hole Quantum Physics
• Phenomenological Description of the Interior of the Schwarzschild Black Hole
• Black hole evaporation and semiclassical thin shell collapse
• Energy-momentum tensor and metric near the Schwarzschild sphere
• Black Hole as a Quantum Field Configuration
• An Analytic Description of Semi-Classical Black-Hole Geometry
• Asymptotic Black Holes
• Trapping Horizon and Negative Energy

Cited by in corpus (5)

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