Dynamics and Observer-Dependence of Holographic Screens

TL;DR

This paper investigates the evolution and observer-dependence of holographic screens, exploring their causal structure, information storage capacity, and how their geometry reflects quantum gravity properties, including in background-free scenarios.

Contribution

It introduces a detailed analysis of holographic screens' dynamics, their observer-dependent nature, and a background-free construction linking screen evolution to spacetime constraints.

Findings

Holographic screens have a nonrelativistic causal structure.

Each leaf can encode all quantum information on a null slice.

Screen ambiguity corresponds to a free function on the screen.

Abstract

We study the evolution of holographic screens, both generally and in explicit examples, including cosmology and gravitational collapse. A screen $H$ consists of a one-parameter sequence of maximal surfaces called leaves. Its causal structure is nonrelativistic. Each leaf can store all of the quantum information on a corresponding null slice holographically, at no more than one bit per Planck area. Therefore, we expect the screen geometry to reflect certain coarse-grained quantities in the quantum gravity theory. In a given spacetime, there are many different screens, which are naturally associated to different observers. We find that this ambiguity corresponds precisely to the free choice of a single function on $H$. We also consider the background-free construction of $H$, where the spacetime is not given. The evolution equations then constrain aspects of the full spacetime and the screen's embedding in it.