Entanglement entropy and the Ricci flow

TL;DR

This paper investigates how the entanglement entropy of a two-dimensional black hole evolves under Ricci flow, revealing its monotonic behavior and linking geometric flow to quantum correlations.

Contribution

It demonstrates that entanglement entropy remains monotonic along the Ricci flow for a 2D black hole, connecting geometric evolution with quantum entanglement.

Findings

Entanglement entropy is monotonic along Ricci flow.

The study links geometric flow to quantum correlations in black holes.

Provides insights into the interplay between geometry and quantum information.

Abstract

We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other is outside the black hole horizon. It is demonstrated that the entanglement entropy is monotonic along the Ricci flow.