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

TL;DR

This paper demonstrates that the averaged null energy condition (ANEC) on null lines follows from the generalized second law of thermodynamics in semiclassical gravity, linking quantum energy conditions to thermodynamic principles.

Contribution

It establishes a proof that the ANEC on null lines is a consequence of the generalized second law, under certain assumptions, connecting quantum energy conditions with thermodynamics in gravity.

Findings

ANEC on null lines follows from the generalized second law

Violations of ANEC on general geodesics do not affect certain theorems

A shear-inclusive generalization of ANEC is proposed and proven

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.