Holographic evolution of the mutual information

TL;DR

This paper investigates the time evolution of holographic mutual information during black hole formation in Vaidya spacetimes, revealing non-monotonic behavior, monogamy, and conditions for entropy inequalities.

Contribution

It provides the first detailed analysis of the dynamical behavior of holographic mutual information in out-of-equilibrium settings with black hole formation.

Findings

Mutual information is non-monotonic over time.

Mutual information remains monogamous in the studied regimes.

Null energy condition is necessary for entropy inequalities.

Abstract

We compute the time evolution of the mutual information in out of equilibrium quantum systems whose gravity duals are Vaidya spacetimes in three and four dimensions, which describe the formation of a black hole through the collapse of null dust. We find the holographic mutual information to be non monotonic in time and always monogamous in the ranges explored. We also find that there is a region in the configuration space where it vanishes at all times. We show that the null energy condition is a necessary condition for both the strong subadditivity of the holographic entanglement entropy and the monogamy of the holographic mutual information.