Proof of the averaged null energy condition in a classical curved spacetime using a null-projected quantum inequality

TL;DR

This paper derives a null-projected quantum inequality for a scalar field in curved spacetime and uses it to prove the averaged null energy condition (ANEC) along achronal geodesics, ruling out certain exotic phenomena.

Contribution

It introduces a null-projected quantum inequality for a massless scalar field in curved spacetime and applies it to prove ANEC under specific geometric conditions.

Findings

Proved ANEC for achronal geodesics in curved spacetime

Derived a quantum inequality for a scalar field to first order in Riemann tensor

Ruling out of exotic phenomena like wormholes under these conditions

Abstract

Quantum inequalities are constraints on how negative the weighted average of the renormalized stress-energy tensor of a quantum field can be. A null-projected quantum inequality can be used to prove the averaged null energy condition (ANEC), which would then rule out exotic phenomena such as wormholes and time machines. In this work we derive such an inequality for a massless minimally coupled scalar field, working to first order of the Riemann tensor and its derivatives. We then use this inequality to prove ANEC on achronal geodesics in a curved background that obeys the null convergence condition.