A moving mirror in AdS space as a toy model for holographic thermalization

TL;DR

This paper introduces a simplified model of holographic thermalization using a moving mirror in AdS space, providing a method to compute two-point functions that aligns with geometric optics predictions.

Contribution

It develops a novel approach to study time-dependent holographic processes by modeling a moving mirror in AdS and calculating scalar two-point functions via WKB approximation.

Findings

The method accurately reproduces the singularity structure of two-point functions.

Tested on two mirror trajectories, results agree with geometric optics.

Provides a new toy model for exploring holographic thermalization.

Abstract

It is expected that thermalization may be described within gauge/gravity duality by considering time-dependent configurations on the gravity side of the correspondence, for instance a gravitational collapse of a matter configuration in Anti-de Sitter space. As a step towards the ambitious goal of describing such a configuration, we investigate a simple time-dependent toy model in which a mirror moves in the radial direction of Anti-de Sitter space. For this configuration, we establish a procedure for calculating two-point functions of scalar fluctuations, based on a WKB approximation. We test our method on two sample trajectories for the mirror, and find that the singularity structure of the two-point functions is in agreement with geometric optics.