RG-2 flow and black hole entanglement entropy

We study the evolution of a metric of a two dimensional black hole under the second loop renormalization group fow, the RG-2 fow. Since the black hole metric is noncompact (we consider it asymptotically flat) we adapt some proofs for the compact case to the asymptotically flat case. We found that the appearance of horizons during the evolution is related to the condition of parabolicity of the flow. We also show that the entanglement entropy of a two dimensional black hole is monotonic under the RG-2 flow. We generalize the results obtained for the first loop approximation and discuss the implications for higher order loops.