  We elaborate on the recent claim [arXiv:1702.03583] that non-perturbative
effects in $\alpha'$, which are at the core of the FZZ duality, render the
region just behind the horizon of the $SL(2,\mathbb{R})_k/U(1)$ black hole
singular already at the classical level ($g_s=0$). We argue that the 2D
classical $SL(2,\mathbb{R})_k/U(1)$ black hole could shed some light on quantum
black holes in higher dimensions including large black holes in $AdS_5\times
S^5$.
