Gravitational Positive Energy Theorems from Information Inequalities

TL;DR

This paper establishes that in asymptotically AdS spacetimes, a family of positive energy conditions can be derived from quantum information inequalities, linking gravitational energy to relative entropy in the dual CFT.

Contribution

It introduces a new family of positive energy theorems in AdS spacetimes based on information-theoretic principles, connecting gravity and quantum information.

Findings

Gravitational energy is non-negative for all boundary regions.

Energy decreases as the boundary region shrinks.

Positivity follows from quantum relative entropy properties.

Abstract

In this paper we argue that classical, asymptotically AdS spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region $B$ of the boundary spacetime, we can associate a bulk spatial region $\Sigma_B$ between $B$ and the bulk extremal surface $\tilde{B}$ with the same boundary as $B$. We show that there exists a natural notion of a gravitational energy for every such region that is non-negative, and non-increasing as one makes the region smaller. The results follow from identifying this gravitational energy with a quantum relative entropy in the associated dual CFT state. The positivity and monotonicity properties of the gravitational energy are implied by the positivity and monotonicity of relative entropy, which holds universally in all quantum systems.