Distance between collapsing matter and trapping horizon in evaporating black holes

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 $\mathrm{\Delta }L$ between the time-like apparent horizon and the surface of the collapsing matter after it has entered the apparent horizon. We show that $\mathrm{\Delta }L$ can never be larger than $\mathcal{O}(n^{3\mathrm{/}2}{\mathrm{\ell }}_p)$ when the black hole is evaporated to $1\mathrm{/}n$ of its initial mass, as long as $n \ll a^{2/3}/\ell_p^{2/3}$(where$a$istheSchwarzschildradiusand$\ell_p$ is the Planck length). For example, the distance between the matter and the apparent horizon must be Planckian at the Page time.