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We compute entanglement entropy and differential entropy in inhomogeneous holographic quenches in AdS3/CFT2. The quenches are arbitrarily inhomogeneous and modeled by an infalling shell of massless nonrotating 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 nonperturbative 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.
Bibliographical note48 pages, 10 figures, v2: various improvements, agrees with published version