Averaged null energy condition in a classical curved background

Abstract

The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. Exotic spacetimes, such as those allow wormholes or the construction of time machines are possible in general relativity only if ANEC is violated along achronal geodesics. Starting from a conjecture that flat-space quantum inequalities apply with small corrections in spacetimes with small curvature, we prove that ANEC is obeyed by a minimally-coupled, free quantum scalar field on any achronal null geodesic surrounded by a tubular neighborhood whose curvature is produced by a classical source.

References in corpus (5)

• Achronal averaged null energy condition
• Absolute quantum energy inequalities in curved spacetime
• Quantum Energy Inequalities for the Non-Minimally Coupled Scalar Field
• Averaged null energy condition in spacetimes with boundaries
• Averaged Energy Inequalities for the Non-Minimally Coupled Classical Scalar Field