Strong subadditivity and the covariant holographic entanglement entropy formula

TL;DR

This paper investigates whether the covariant holographic entanglement entropy formula obeys strong subadditivity in dynamic spacetimes, finding it does under certain energy conditions, thus supporting its validity.

Contribution

It demonstrates that the covariant HRT entanglement entropy formula satisfies strong subadditivity in AdS-Vaidya spacetimes when the null energy condition holds.

Findings

SSA is obeyed in AdS-Vaidya spacetimes under null energy condition

Supports the validity of the covariant HRT formula in dynamic backgrounds

Provides evidence for the fundamental property of entropy in holographic contexts

Abstract

Headrick and Takayanagi showed that the Ryu-Takayanagi holographic entanglement entropy formula generally obeys the strong subadditivity (SSA) inequality, a fundamental property of entropy. However, the Ryu-Takayanagi formula only applies when the bulk spacetime is static. It is not known whether the covariant generalization proposed by Hubeny, Rangamani, and Takayanagi (HRT) also obeys SSA. We investigate this question in three-dimensional AdS-Vaidya spacetimes, finding that SSA is obeyed as long as the bulk spacetime satisfies the null energy condition. This provides strong support for the validity of the HRT formula.