Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law

Abstract

A null line is a complete achronal null geodesic. It is proven that for any quantum fields minimally coupled to semiclassical Einstein gravity, the averaged null energy condition (ANEC) on null lines is a consequence of the generalized second law of thermodynamics for causal horizons. Auxiliary assumptions include CPT and the existence of a suitable renormalization scheme for the generalized entropy. Although the ANEC can be violated on general geodesics in curved spacetimes, as long as the ANEC holds on null lines there exist theorems showing that semiclassical gravity should satisfy positivity of energy, topological censorship, and should not admit closed timelike curves. It is pointed out that these theorems fail once the linearized graviton field is quantized, because then the renormalized shear squared term in the Raychaudhuri equation can be negative. A "shear-inclusive" generalization of the ANEC is proposed to remedy this, and is proven under an additional assumption about perturbations to horizons in classical general relativity.

19 pages, 1 figure. Added 2 paragraphs to end of section 2

References in corpus (4)

• Achronal averaged null energy condition
• Ten Proofs of the Generalized Second Law
• Quantum Energy Inequalities and local covariance I: Globally hyperbolic spacetimes
• Chronological spacetimes without lightlike lines are stably causal

Cited by in corpus (36)

• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Traversable Wormholes via a Double Trace Deformation
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Averaged Null Energy Condition from Causality
• A Primer on Energy Conditions
• Energy conditions in general relativity and quantum field theory
• A General Proof of the Quantum Null Energy Condition
• The Generalized Second Law implies a Quantum Singularity Theorem
• A perturbative perspective on self-supporting wormholes
• A holographic proof of the averaged null energy condition
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Can scale-dependent cosmology alleviate the $H_0$ tension?
• A Lower Bound on the Energy Density in Classical and Quantum Field Theories
• Rotating traversable wormholes in AdS
• Light-ray operators, detectors and gravitational event shapes
• The Quantum Null Energy Condition, Entanglement Wedge Nesting, and Quantum Focusing
• Geometric Constraints from Subregion Duality Beyond the Classical Regime
• Thermodynamic Origin of the Null Energy Condition
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Simple Perturbatively Traversable Wormholes from Bulk Fermions
• The sounds of science: a symphony for many instruments and voices
• A gravitational collapse singularity theorem consistent with black hole evaporation
• Global aspects of conformal symmetry and the ANEC in dS and AdS
• Eternal Universes
• Black hole-wormhole collisions and the emergence of islands
• Self-supporting wormholes with massive vector field
• How Much NEC Breaking Can the Universe Endure?
• Holography of negative energy states
• The fermionic double smeared null energy condition
• Renormalized Quantum Stress-Energy Tensor of a Nonzero Radius Cosmic String
• Open case for a closed universe
• Self-Supporting Wormholes in Four Dimensions with Scalar Field
• Dynamical Horizons and Black Hole Soft Hair
• Geodesically Complete Curvature-Bounce Inflation
• Positive Mass in General Relativity Without Energy Conditions
• Schwarzschild Quantum Fluctuations from Regge-Wheeler Scattering