Universality in holographic entropy production

TL;DR

This paper studies the time evolution of holographic entanglement entropy and causal holographic information during thermalization, revealing universal linear growth behavior and providing a detailed dynamical analysis with new coordinate and matching condition constructions.

Contribution

It provides a full dynamical treatment of holographic entropy evolution, including varying shell parameters, and demonstrates universal linear growth in entanglement entropy during thermalization.

Findings

Universal linear growth of entanglement entropy during thermalization.

Explicit construction of coordinate system continuous at the thin shell.

Derivation of matching conditions for extremal surfaces crossing the shell.

Abstract

We consider the time evolution of two entropy-like quantities, the holographic entanglement entropy and causal holographic information, in a model of holographic thermalization dual to the gravitational collapse of a thin planar shell. Unlike earlier calculations valid in different limits, we perform a full treatment of the dynamics of the system, varying both the shell's equation of state and initial position. In all cases considered, we find that between an early period related to the acceleration of the shell and a late epoch of saturation towards the thermal limit, the entanglement entropy exhibits universal linear growth in time in accordance with the prediction of Liu and Suh. As intermediate steps of our analysis, we explicitly construct a coordinate system continuous at the location of an infinitely thin shell and derive matching conditions for geodesics and extremal surfaces traversing this region.