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The potential behind the horizon of an eternal black hole in classical theories is described in terms of data that is available to an external observer -- the reflection coefficient of a wave that scatters on the black hole.
- In GR and perturbative string theory (in $\alpha'$), the potential is regular at the horizon and it blows up at the singularity.
- The exact reflection coefficient, that is known for the $SL(2,\mathbb{R})_k/U(1)$ black hole and includes non-perturbative $\alpha'$ effects, seems however to imply that there is a highly non-trivial structure just behind the horizon.
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