Time Evolution of Entanglement Entropy from Black Hole Interiors

TL;DR

This paper studies how entanglement entropy evolves over time in conformal field theories dual to black hole spacetimes, revealing linear growth linked to black hole interior expansion and matching bulk-boundary calculations.

Contribution

It provides a detailed analysis of time-dependent entanglement entropy in holographic setups, connecting interior geometry growth with entropy increase, including explicit calculations for 2D CFTs.

Findings

Entanglement entropy grows linearly with time in the studied states.

Bulk and boundary computations of entanglement entropy agree in 2D CFTs.

Exponential decay of correlators is explained by interior geometry growth.

Abstract

We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.