Quantum inequality in spacetimes with small curvature

Abstract

Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to disprove the existence of exotic phenomena, such as closed timelike curves. In this work we derive such an inequality for a minimally-coupled scalar field on a geodesic in a spacetime with small curvature, working to first order in the Ricci tensor and its derivatives. Since only the Ricci tensor enters, there are no first-order corrections to the flat-space quantum inequalities on paths which do not encounter any matter or energy.

21 pages

References in corpus (15)

• The motion of point particles in curved spacetime
• Quantum Field Theory Constrains Traversable Wormhole Geometries
• Bounds on negative energy densities in flat spacetime
• Gravitational vacuum polarization II: Energy conditions in the Boulware vacuum
• A general worldline quantum inequality
• The unphysical nature of "Warp Drive"
• Achronal averaged null energy condition
• Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator
• Gravitational vacuum polarization I: Energy conditions in the Hartle--Hawking vacuum
• Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum
• Null energy conditions in quantum field theory
• Absolute quantum energy inequalities in curved spacetime
• van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes
• Averaged null energy condition in a classical curved background
• Quantum inequality for a scalar field with a background potential

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• A semiclassical singularity theorem
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Pandora's box lid: geometry near the apparent horizon
• Universal properties of the near-horizon geometry
• A new derivation of singularity theorems with weakened energy hypotheses
• Kerr-Vaidya black holes
• Physical black holes in fourth-order gravity
• Spherically symmetric black holes in metric gravity
• Inaccessibility of traversable wormholes
• Physical black holes in semiclassical gravity
• Wormhole restrictions from quantum energy inequalities
• Averaged null energy condition and quantum inequalities in curved spacetime
• Quantum Energy Inequalities along stationary worldlines
• Black holes and their horizons in semiclassical and modified theories of gravity