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

中文翻译：

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RG-2 流动与黑洞纠缠熵

我们研究了欧几里得二维黑洞度量在第二个循环重整化群流 RG-2 流下的演化。由于黑洞度量是非紧凑的（我们认为它是渐近平坦的），我们将紧凑情况的一些证明适应于渐近平坦情况。我们发现演化过程中视界的出现与流动的抛物线条件有关。我们还表明，二维欧几里得史瓦西黑洞的纠缠熵在 RG-2 流下是单调的。我们概括了第一次循环近似获得的结果，并讨论了对高阶循环的影响