# Entanglement entropy in inhomogeneous quenches in AdS$_3$/CFT$_2$

## TL;DR

This paper analyzes how entanglement entropy evolves in inhomogeneous holographic quenches in AdS3/CFT2, revealing complex behaviors like plateaus and bumps, with both analytical and numerical methods applied to specific examples.

## Contribution

It introduces a framework for computing entanglement entropy in inhomogeneous quenches with time-dependent stress-energy, including analytical perturbative and numerical non-perturbative results.

## Key findings

- Entanglement entropy exhibits saturation, plateaus, bumps, and derivative discontinuities.
- Both oscillatory and bilocal quenches show non-thermal steady states.
- Analytical solutions are obtained for small inhomogeneities, numerical for larger ones.

## Abstract

We compute entanglement entropy and differential entropy in inhomogeneous holographic quenches in AdS$_3$/CFT$_2$. The quenches are arbitrarily inhomogeneous and modeled by an infalling shell of massless non-rotating matter where the final state is not dual to a static black hole but rather to a black hole with time-dependent stress-energy tensor modes. We study the entanglement entropy of an interval and differential entropy of a family of intervals analytically when the inhomogeneities have a perturbative amplitude and numerically for non-perturbative inhomogeneities. While we are in principle able to study these quantities for any inhomogeneities, we discuss two concrete examples: an oscillatory quench and a bilocal quench. Both cases display saturation towards a steady state but do not fully thermalize. Depending on the location and size of the interval, the entanglement entropy displays a variety of interesting phenomena such as plateau phases, bumps, and discontinuities in its first derivative with respect to time.