On volume subregion complexity in Vaidya spacetime

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.

22 pages, 9 figures; V2: expanded discussion