Page Curves and Bath Deformations

TL;DR

This paper investigates how relevant scalar deformations in a holographic setup affect the Page curve and entanglement dynamics of black holes, revealing that RG flow influences information retrieval times.

Contribution

It introduces a holographic model with bath deformations that alter the Page curve, linking RG flow to black hole information retrieval.

Findings

Deformation changes the Page time and curve shape.

Two scales control coarse-graining and entanglement dynamics.

Higher Page time correlates with increased bath coarse-graining.

Abstract

We study the black hole information problem within a semiclassically gravitating AdS$_d$ black hole coupled to and in equilibrium with a $d$-dimensional thermal conformal bath. We deform the bath state by a relevant scalar deformation, triggering a holographic RG flow whose "trans-IR" region deforms from a Schwarzschild geometry to a Kasner universe. The setup manifests two independent scales which control both the extent of coarse-graining and the entanglement dynamics when counting Hawking degrees of freedom in the bath. In tuning either, we find nontrivial changes to the Page time and Page curve. We consequently view the Page curve as a probe of the holographic RG flow, with a higher Page time manifesting as a result of increased coarse-graining of the bath degrees of freedom.