Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining

Understand

We argue that the entanglement entropy offers us a useful coarse-grained entropy in time-dependent AdS/CFT.

• We show that the total von-Neumann entropy remains vanishing even when a black hole is created in a gravity dual, being consistent with the fact that its corresponding CFT is described by a time-dependent pure state.
• We analytically calculate the time evolution of entanglement entropy for a free Dirac fermion on a circle following a quantum quench.
• This is interpreted as a toy holographic dual of black hole creations and annihilations.