Page Curves and Bath Deformations

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.

Trans-IR Flows to Black Hole Singularities

“…While a T is stationary at both the boundary (the UV) and the horizon (the IR), it is still monotonic even along the trans-IR flow, thus satisfying an extension of the holographic a-theorem [9,10] to complex energy scales. With emphasis on "free Kasner flows" [1,11], we find a T → 0 at the singularity (the trans-IR endpoint). In other words, all degrees of freedom are lost at the singularity.…”

“…6 Furthermore r < r h is the exterior (F (r) > 0), while r > r h is the interior (F (r) < 0). The resulting metric is the Schwarzschildlike one of [1,11],…”

“…Thus, we can answer (Q2) by analyzing how the near-singularity geometry is affected by backreaction. Describing backreaction is more easily done after specifying the matter sector, so we focus on the minimal model of [1,11]-Einstein gravity with a free massive scalar. In the resulting flows, we will find that a T → 0 at the singularity, around which the local geometry is that of a Kasner universe [32][33][34].…”

“…To solve ( 25)-( 27) numerically, we expand {F, χ, φ} around the horizon r = r h then perform a two-sided shooting method towards both the boundary r = 0 and the singularity r = ∞. The mathematical details are in [11]. The near-singularity geometry is a Kasner universe,…”

“…This expression is more meaningful if it is written in terms of the Kasner exponent p t , which is directly related to q in the literature [1,11]. For any d,…”