Scale anomalies imply violation of the averaged null energy condition

Abstract

Considerable interest has recently been expressed regarding the issue of whether or not quantum field theory on a fixed but curved background spacetime satisfies the averaged null energy condition (ANEC). A comment by Wald and Yurtsever [Phys. Rev. D43, 403 (1991)] indicates that in general the answer is no. In this note I explore this issue in more detail, and succeed in characterizing a broad class of spacetimes in which the ANEC is guaranteed to be violated. Finally, I add some comments regarding ANEC violation in Schwarzschild spacetime.

6 pages; ReV_TeX 3.0]

Cited by in corpus (60)

• Black-bounce to traversable wormhole
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Energy conditions in general relativity and quantum field theory
• Quantum Field Theory Constrains Traversable Wormhole Geometries
• General Relativistic Energy Conditions: The Hubble expansion in the epoch of galaxy formation
• Primordial perturbations in a non singular bouncing universe model
• Restrictions on Negative Energy Density in Flat Spacetime
• Gravitational vacuum polarization II: Energy conditions in the Boulware vacuum
• On the collision of two shock waves in AdS5
• Anisotropic Cosmological Constant and the CMB Quadrupole Anomaly
• Achronal averaged null energy condition
• Passing through the bounce in the ekpyrotic models
• Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum
• Gravitational vacuum polarization I: Energy conditions in the Hartle--Hawking vacuum
• Vaidya spacetimes, black-bounces, and traversable wormholes
• Superluminal censorship
• Graceful Exit and Energy Conditions in String Cosmology
• Semiclassical energy conditions for quantum vacuum states
• Classical and quantum flux energy conditions for quantum vacuum states
• Might some gamma ray bursts be an observable signature of natural wormholes?
• Averaged Energy Conditions and Evaporating Black Holes
• Non-singular big-bounces and evolution of linear fluctuations
• Regge-Wheeler equation, linear stability, and greybody factors for dirty black holes
• Tolman wormholes violate the strong energy condition
• Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
• Constraints on Spatial distributions of Negative Energy
• Has the Universe always expanded ?
• Generic warp drives violate the null energy condition
• Averaged null energy condition violation in a conformally flat spacetime
• The averaged null energy condition for general quantum field theories in two dimensions
• Focusing and the Holographic Hypothesis
• Essential core of the Hawking--Ellis types
• Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds
• Averaged null energy condition in a classical curved background
• Rotating black holes in semiclassical gravity
• Generalized Rainich conditions, generalized stress-energy conditions, and the Hawking-Ellis classification
• Quantum Interest in (3+1) dimensional Minkowski space
• Time-dependent AdS/CFT correspondence and the Quark-Gluon plasma
• Spacetime Averaged Null Energy Condition
• Quantum Spacetime Instability and Breakdown of Semiclassical Gravity
• Conformally invariant averaged null energy condition from AdS/CFT
• Achronal ANEC, Weak Cosmic Censorship, and AdS/CFT duality
• Global aspects of conformal symmetry and the ANEC in dS and AdS
• Black holes, white holes, and near-horizon physics
• $<T_{\nu }^{\mu }{>}_{ren}$ of the quantized fields in the Unruh state in the Schwarzschild spacetime
• Restrictions on negative energy density in a curved spacetime
• Classical and semi-classical energy conditions
• Regularization versus renormalization: Why are Casimir energy differences so often finite?
• Hawking-Ellis type III spacetime geometry
• Does anomalous violation of null energy condition invalidate holographic c-theorem?
• Averaged Energy Conditions in 4D Evaporating Black Hole Backgrounds
• Bouncing universes and their perturbations : a simple model revisited
• Wormhole restrictions from quantum energy inequalities
• On a macroscopic traversable spacewarp in practice
• Averaged null energy condition and quantum inequalities in curved spacetime
• The energy conditions and model selection in the local Universe
• Black Hole Complementarity and ER/EPR
• Tractor beams, pressor beams, and stressor beams in general relativity
• Spacetime Instability and Quantum Gravity as Low Energy Effective Field Theory
• Classification of quantum states based on the null energy condition