# Holographic Subregion Complexity in General Vaidya Geometry

## TL;DR

This paper explores the evolution of holographic subregion complexity in Vaidya-AdS spacetime, identifying three stages of linear growth and decay, and compares growth rates with the Lloyd bound, revealing differences between CV and subregion CV conjectures.

## Contribution

It provides a detailed analysis of subregion complexity evolution in Vaidya spacetime, highlighting distinct growth stages and their relation to the Lloyd bound, and compares different holographic complexity proposals.

## Key findings

- Three distinct stages of HSC evolution identified
- Growth rates at early and intermediate times compared with Lloyd bound
- Differences observed between CV and subregion CV conjectures in Vaidya spacetime

## Abstract

We investigate general features of the evolution of holographic subregion complexity (HSC) on Vaidya-AdS metric with a general form. The spacetime is dual to a sudden quench process in quantum system and HSC is a measure of the ``difference'' between two mixed states. Based on the subregion CV (Complexity equals Volume) conjecture and in the large size limit, we extract out three distinct stages during the evolution of HSC: the stage of linear growth at the early time, the stage of linear growth with a slightly small rate during the intermediate time and the stage of linear decrease at the late time. The growth rates of the first two stages are compared with the Lloyd bound. We find that with some choices of certain parameter, the Lloyd bound is always saturated at the early time, while at the intermediate stage, the growth rate is always less than the Lloyd bound. Moreover, the fact that the behavior of CV conjecture and its version of the subregion in Vaidya spacetime implies that they are different even in the large size limit.