Remarks on Thermal Strings outside Black Holes

We discuss the semiclassical approximation to the level density of (super) strings propagating in non-compact coset manifolds G/H. We show that the WKB ansatz agrees with heuristic red-shift arguments with respect to the “exact” sigma-model metric, up to some deviations from minimal coupling, parametrized by the dilaton. This approximation is used to study thermal ensembles of free strings in black holes, with the “brick wall” horizon regularization of ’t Hooft. In two dimensions the entropy diverges logarithmically with the horizon thickness, and a local Hagedorn transition occurs in higher dimensional models. We also observe that supersymmetry improves the regularity of strings at the horizon.