# RG-2 flow and black hole entanglement entropy

## TL;DR

This paper investigates how the metric of a two-dimensional asymptotically flat black hole evolves under the second loop renormalization group flow, revealing horizon formation conditions and demonstrating the monotonic behavior of entanglement entropy.

## Contribution

It extends the analysis of black hole evolution under RG flow to the second loop level and adapts proofs for asymptotically flat spacetimes, highlighting horizon conditions and entropy monotonicity.

## Key findings

- Horizon formation is linked to parabolicity of the flow.
- Entanglement entropy decreases monotonically under RG-2 flow.
- Results generalize first loop approximation to higher loops.

## Abstract

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.

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Source: https://tomesphere.com/paper/1905.00102