Holographic Complexity for Time-Dependent Backgrounds

TL;DR

This paper investigates how holographic complexity evolves in time-dependent asymptotically AdS geometries by defining a volume-based measure using covariant slices, extending static complexity concepts to dynamic backgrounds.

Contribution

It introduces a method to compute holographic complexity in time-dependent backgrounds using covariant zero mean curvature slices and minimal surfaces, generalizing static complexity measures.

Findings

Derived a volume-based definition of time-dependent holographic complexity.

Analyzed the complexity as a perturbation of static AdS geometries.

Provided a framework for calculating complexity in dynamic spacetimes.

Abstract

In this paper, we will analyse the holographic complexity for time-dependent asymptotically $AdS$ geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension one spacelike slice of the bulk spacetime to define a co-dimension two minimal surface. The time-dependent holographic complexity will be defined using the volume enclosed by this minimal surface. This time-dependent holographic complexity will reduce to the usual holographic complexity for static geometries. We will analyse the time-dependence as a perturbation of the asymptotically $AdS$ geometries. Thus, we will obtain time-dependent asymptotically $AdS$ geometries, and we will calculate the holographic complexity for such a time-dependent geometries.