Cosmological singularities, entanglement and quantum extremal surfaces

TL;DR

The paper investigates how entanglement and extremal surfaces behave in spacetimes with cosmological Big-Crunch singularities, combining classical RT/HRT analyses in isotropic AdS Kasner with 2D dilaton-gravity reductions and quantum extremal surface calculations. It shows that classical extremal surfaces bending away from the singularity persist in the semiclassical regime, while quantum extremal surfaces in the 2D cosmologies are driven to the semiclassical region far from the singularity, with no islands appearing in these models. The results suggest a maximin-like entanglement structure that avoids the singular region, consistent with Page-curve expectations for information recovery. The study highlights the limits of probing near-singularity physics via entanglement in these holographic cosmologies and points to future work on more general cosmologies, bulk states, and near-singularity physics.

Abstract

We study aspects of entanglement and extremal surfaces in various families of spacetimes exhibiting cosmological, Big-Crunch, singularities, in particular isotropic $AdS$ Kasner. The classical extremal surface dips into the bulk radial and time directions. Explicitly analysing the extremization equations in the semiclassical region far from the singularity, we find the surface bends in the direction away from the singularity. In the 2-dim cosmologies obtained by dimensional reduction of these and other singularities, we have studied quantum extremal surfaces by extremizing the generalized entropy. The resulting extremization shows the quantum extremal surfaces to always be driven to the semiclassical region far from the singularity. We give some comments and speculations on our analysis.

Figures (3)

• Figure 1: Cartoon of extremal surfaces in $AdS$ Kasner, anchored on a boundary time slice (black curve). For small width (blue), the surface stays close to the boundary, while for large size (red), the surface dips deeper into the bulk. These bend away from the singularity (dotted line).
• Figure 2: Cartoon of the local geometry of the extremal surface near the turning point $(r_*, t_*)$. The surface is anchored on a time slice $t_0$ far from the singularity at $t=0$ (not shown). It dips in the direction away from the singularity.
• Figure 3: Cartoon of the 2-dim geometry, the holographic boundary at $r=0$ and the QES at $(t_*,r_*)$. The solid blue line is the spatial interval between the boundary observer and the QES. The singularity is at $t=0$ far up (not shown). The extremization drives the QES location to $t_*\rightarrow\infty$ (far from the singularity) and $r_*\rightarrow\infty$ (which is the left vertical line).