Black Hole Multi-Entropy Curves

TL;DR

This paper introduces a multi-entropy curve for black holes, capturing complex entanglement structures during evaporation, revealing non-zero residual entanglement that extends beyond traditional entropy measures.

Contribution

It generalizes the Page curve to multi-partite entanglement, providing new insights into black hole information retention and entanglement structure during evaporation.

Findings

Multi-entropy increases initially, peaks after Page time, then decreases.

Multi-entropy does not vanish at the end, indicating residual entanglement.

The curve extends the understanding of black hole information dynamics.

Abstract

We investigate the multi-partite entanglement structure of an evaporating black hole and its Hawking radiation by dividing the radiation into finer subsystems. We approximate an evaporating black hole and its radiation with a Haar-random state for this purpose. Using the multi-entropy of these configurations, we define a black hole multi-entropy curve, which describes how the multi-entropy changes during the black hole evaporation. This black hole multi-entropy curve is a natural generalization of the Page curve since the multi-entropy reduces to the entanglement entropy for the bi-partite case. The multi-entropy curve keeps increasing in the early time. It reaches the maximum value at the multi-entropy time, which is later than the Page time, and starts to decrease. However, it does not decrease to zero at the end of the black hole evaporation. This non-zero value of the multi-entropy represents the secret entanglement between Hawking particles.