Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining

TL;DR

This paper explores how entanglement entropy can serve as a coarse-grained measure in time-dependent holographic duals, demonstrating its effectiveness in tracking black hole formation without encountering the information paradox.

Contribution

It introduces entanglement entropy as a useful coarse-grained entropy in dynamic AdS/CFT scenarios and provides an analytical model for black hole creation and annihilation.

Findings

Total von-Neumann entropy remains zero during black hole formation.

Analytical calculation of entanglement entropy evolution after a quantum quench.

Model is free from the black hole information paradox.

Abstract

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. It is manifestly free from the black hole information problem.