Gravitational Positive Energy Theorems from Information Inequalities

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.

References in corpus (3)

• Towards a derivation of holographic entanglement entropy
• Notes on the K3 Surface and the Mathieu group M_24
• Relative Entropies in Conformal Field Theory

Cited by in corpus (34)

• The Ryu-Takayanagi Formula from Quantum Error Correction
• Aspects of general higher-order gravities
• Complexity and the bulk volume, a new York time story
• Quantum Information in Holographic Duality
• Gravity Degrees of Freedom on a Null Surface
• Connecting Fisher information to bulk entanglement in holography
• Swing surfaces and holographic entanglement beyond AdS/CFT
• Constraining Quantum Fields using Modular Theory
• Modular Flow of Excited States
• Bulk entanglement entropy in perturbative excited states
• Null infinity as an open Hamiltonian system
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Gravity Dual of Connes Cocycle Flow
• Surface Theory: the Classical, the Quantum, and the Holographic
• Symmetries, charges and conservation laws at causal diamonds in general relativity
• Higher Curvature Gravity from Entanglement in Conformal Field Theories
• Holographic second laws of black hole thermodynamics
• The holographic entropy zoo
• Gravitation in flat spacetime from entanglement
• Reflected Entropy in AdS${}_3$/WCFT
• Quantum tasks in holography
• Complete Einstein equation from the generalized First Law of Entanglement
• Entanglement asymmetry in conformal field theory and holography
• Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
• Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
• Positive gravitational subsystem energies from CFT cone relative entropies
• Chaos and relative entropy
• The holographic dual of Rényi relative entropy
• Anomalous Gravitation and its Positivity from Entanglement
• Numerical calculations on the relative entanglement entropy in critical spin chains
• Bulk Matter and the Boundary Quantum Null Energy Condition
• Brane dynamics from the first law of entanglement
• Pseudo-topological Quasi-local Energy of Torsion Gravity
• Generalized Off-Shell ADT Conserved Charges in the Presence of Matter Chern-Simons Term