Page curves and bath deformations

We study the black hole information problem within a semiclassically gravitating AdSd 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.

Automated summary

In this study, we investigate the black hole information problem in a semiclassical gravitating AdSd black hole coupled to a d-dimensional thermal conformal bath. By deforming the bath state through a relevant scalar deformation, a holographic RG flow is triggered, causing the trans-IR region to transition from a Schwarzschild geometry to a Kasner universe. The setup exhibits two independent scales that control the extent of coarse-graining and the entanglement dynamics when counting Hawking degrees of freedom in the bath. Tuning either scale results in nontrivial changes to the Page time and Page curve.