RG-2 flow and black hole entanglement entropy

We study the evolution of a Euclidean two-dimensional black hole metric under the second loop renormalization group flow, the RG-2 flow. Since the black hole metric is non-compact (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 parabolicity condition of the flow. We also show that the entanglement entropy of the two-dimensional Euclidean Schwarzschild 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