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

RG-2 flow and black hole entanglement entropy