2015/07/22 by Eleni-Alexandra Kontou, Kontou, Eleni-Alexandra
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1507.06299
openalex publication_date 2015/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Averaged Null Energy Condition (ANEC) states that the integral along a\ncomplete null geodesic of the projection of the stress-energy tensor onto the\ntangent vector to the geodesic cannot be negative. ANEC can be used to rule out\nspacetimes with exotic phenomena, such as closed timelike curves, superluminal\ntravel and wormholes. We prove that ANEC is obeyed by a minimally-coupled, free\nquantum scalar field on any achronal null geodesic (not two points can be\nconnected with a timelike curve) surrounded by a tubular neighborhood whose\ncurvature is produced by a classical source. To prove ANEC we use a\nnull-projected quantum inequality, which provides constraints on how negative\nthe weighted average of the renormalized stress-energy tensor of a quantum\nfield can be. Starting with a general result of Fewster and Smith, we first\nderive a timelike projected quantum inequality for a minimally-coupled scalar\nfield on flat spacetime with a background potential. Using that result we\nproceed to find the bound of a quantum inequality on a geodesic in a spacetime\nwith small curvature, working to first order in the Ricci tensor and its\nderivatives. The last step is to derive a bound for the null-projected quantum\ninequality on a general timelike path. Finally we use that result to prove\nachronal ANEC in spacetimes with small curvature.\n