Thermalization of Causal Holographic Information

TL;DR

This paper investigates the behavior of causal holographic information (CHI) in dynamic AdS spacetimes, demonstrating its causal evolution under certain conditions and comparing it with holographic entanglement entropy.

Contribution

It provides a detailed analysis of CHI's causal properties in time-dependent backgrounds, especially during null dust collapse, and compares its behavior with entanglement entropy.

Findings

CHI can be causal in specific sub-regions in time-dependent backgrounds.

The early time growth and late time saturation of CHI and entanglement entropy are derived.

CHI exhibits quasi-teleological behavior but can be entirely causal under certain conditions.

Abstract

We study causal wedges associated with a given sub-region in the boundary of asymptotically AdS spacetimes. Part of our motivation is to better understand the recently proposed holographic observable, causal holographic information (CHI), which is given by the area of a bulk co-dimension two surface lying on the boundary of the causal wedge. It has been suggested that CHI captures the basic amount of information contained in the reduced density matrix about the bulk geometry. To explore its properties further we examine its behaviour in time-dependent situations. As a simple model we focus on null dust collapse in an asymptotically AdS spacetime, modeled by the Vaidya-AdS geometry. We argue that while CHI is generically quasi-telelogical in time-dependent backgrounds, for suitable choice of sub-regions in conformal field theories, the temporal evolution of CHI is entirely causal. We comment on the implications of this observation and more generally on features of causal constructions and contrast our results with the behaviour of holographic entanglement entropy. Along the way we also derive the rate of early time growth and late time saturation (to the thermal value) of both CHI and entanglement entropy in these backgrounds.