Entanglement entropy evolution during gravitational collapse

TL;DR

This paper studies how the entanglement entropy of a scalar field evolves during gravitational collapse, revealing complex scaling behavior and deviations from the area law near horizons in a dynamic spacetime.

Contribution

It introduces a method to compute time-dependent entanglement entropy during gravitational collapse using an Ermakov-like equation, providing new insights into quantum field behavior in evolving black hole spacetimes.

Findings

Entanglement entropy shows nontrivial scaling during collapse

Deviations from the area law occur near the horizon

Results offer insights into quantum entanglement in dynamic gravity

Abstract

We investigate the dynamics of the ground state entanglement entropy for a discretized scalar field propagating within the Oppenheimer-Snyder collapse metric. Starting from a well-controlled initial configuration, we follow the system as it evolves toward the formation of a horizon and, eventually, a singularity. Our approach employs an Ermakov-like equation to determine the time-dependent ground state of the field and calculates the resulting entanglement entropy by tracing out the degrees of freedom inside a spherical region within the matter sphere. We find that the entanglement entropy exhibits nontrivial scaling and time dependence during collapse. Close to the horizon, the entropy can deviate from the simple area law, reflecting the rapid changes in geometry and field configuration. Although the model is idealized, these results provide insights into the generation and scaling of entanglement in the presence of realistic, dynamically evolving gravitational fields.