On volume subregion complexity in Vaidya spacetime

TL;DR

This paper investigates how the volume complexity of a subregion evolves over time in a Vaidya spacetime, modeling a quench-induced thermalization process in a dual conformal field theory, using numerical and analytical methods.

Contribution

It provides the first detailed analysis of subregion volume complexity dynamics in Vaidya spacetime, combining numerical solutions with approximate analytical expressions.

Findings

Time-dependent extremal volume surfaces are computed numerically.

Analytical expressions describe early and late time behavior.

Results illuminate complexity growth during thermalization.

Abstract

We study holographic subregion volume complexity for a line segment in the AdS$_3$ Vaidya geometry. On the field theory side, this gravity background corresponds to a sudden quench which leads to the thermalization of the strongly-coupled dual conformal field theory. We find the time-dependent extremal volume surface by numerically solving a partial differential equation with boundary condition given by the Hubeny-Rangamani-Takayanagi surface, and we use this solution to compute holographic subregion complexity as a function of time. Approximate analytical expressions valid at early and at late times are derived.