Page Curve and the Information Paradox in Flat Space

TL;DR

This paper extends the concept of entanglement wedges and the Page curve to flat space holography using asymptotic causal diamonds, providing new insights into the information paradox without relying on AdS geometry.

Contribution

It introduces flat space analogues of quantum extremal surfaces and entanglement wedges, demonstrating phase transitions at the Page time and connecting flat space holography with entanglement entropy.

Findings

Entanglement wedge phase transition occurs at the Page time in flat space black holes.

Flat space entanglement entropy of ACDs is well-defined and instructive.

The results parallel AdS observations, suggesting universality of entanglement wedge dynamics.

Abstract

Asymptotic Causal Diamonds (ACDs) are a natural flat space analogue of AdS causal wedges, and it has been argued previously that they may be useful for understanding bulk locality in flat space holography. In this paper, we use ACD-inspired ideas to argue that there exist natural candidates for Quantum Extremal Surfaces (QES) and entanglement wedges in flat space, anchored to the conformal boundary. When there is a holographic screen at finite radius, we can also associate entanglement wedges and entropies to screen sub-regions, with the system naturally coupled to a sink. The screen and the boundary provide two complementary ways of formulating the information paradox. We explain how they are related and show that in both formulations, the flat space entanglement wedge undergoes a phase transition at the Page time in the background of an evaporating Schwarzschild black hole. Our results closely parallel recent observations in AdS, and reproduce the Page curve. That there is a variation of the argument that can be phrased directly in flat space without reliance on AdS, is a strong indication that entanglement wedge phase transitions may be key to the information paradox in flat space as well. Along the way, we give evidence that the entanglement entropy of an ACD is a well-defined, and likely instructive, quantity. We further note that the picture of the sink we present here may have an understanding in terms of sub-matrix deconfinement in a large-$N$ setting.