Strong Subadditivity, Null Energy Condition and Charged Black Holes

TL;DR

This paper explores the relationship between the null energy condition in the bulk and the strong sub-additivity of entanglement entropy in the boundary theory within the AdS/CFT framework, revealing conditions under which SSA can be violated.

Contribution

It demonstrates how the violation of the null energy condition in certain bulk geometries correlates with the violation of strong sub-additivity in the boundary entanglement entropy, linking bulk energy conditions to boundary quantum information properties.

Findings

Existence of a critical surface where NEC violation occurs.

Extremal surfaces penetrate forbidden regions only for specific mass and charge functions.

SSA violation correlates with the position of the critical surface relative to the apparent horizon.

Abstract

Using the Hubeny-Rangamani-Takayanagi (HRT) conjectured formula for entanglement entropy in the context of the AdS/CFT correspondence with time-dependent backgrounds, we investigate the relation between the bulk null energy condition (NEC) of the stress-energy tensor with the strong sub-additivity (SSA) property of entanglement entropy in the boundary theory. In a background that interpolates between an AdS to an AdS-Reissner-Nordstrom-type geometry, we find that generically there always exists a critical surface beyond which the violation of NEC would naively occur. However, the extremal area surfaces that determine the entanglement entropy for the boundary theory, can penetrate into this forbidden region only for certain choices for the mass and the charge functions in the background. This penetration is then perceived as the violation of SSA in the boundary theory. We also find that this happens only when the critical surface lies above the apparent horizon, but not otherwise. We conjecture that SSA, which is thus non-trivially related to NEC, also characterizes the entire time-evolution process along which the dual field theory may thermalize.