Localization of Negative Energy and the Bekenstein Bound

TL;DR

A new form of the Bekenstein bound is proved based on the monotonicity of the relative entropy, involving a "free" entropy enclosed in a region which is highly insensitive to space-time entanglement, and it is shown that it further improves the negative energy localization bound.

Abstract

A simple argument shows that negative energy cannot be isolated far away from positive energy in a conformal field theory and strongly constrains its possible dispersal. This is also required by consistency with the Bekenstein bound written in terms of the positivity of relative entropy. We prove a new form of the Bekenstein bound based on the monotonicity of the relative entropy, involving a "free" entropy enclosed in a region which is highly insensitive to space-time entanglement, and show that it further improves the negative energy localization bound.

Figures (1)

• Figure 1: Two spatial spheres $A$ of radius $R_1$ and $B$ of radius $R_2$ located on the past light cone. $S_f(A,B)$ is a measure of entropy crossing the null cone in between the boundaries of $A$ and $B$.