Dynamical Instability of a two-dimensional Quantum Black Hole
  We investigate dynamical instability of a two-dimensional quantum black hole model considered by Lowe in his study of Hawking evaporation. The model is supposed to express a black hole in equilibrium with a bath of Hawking radiation. It turns out that the model has at least one instability modes for a wide range of parameters, and thus it is unstable. 
Y. Itoh, M. Hotta, M. Morikawa and T. Futamase