A semiclassical singularity theorem

Abstract

Quantum fields do not satisfy the pointwise energy conditions that are assumed in the original singularity theorems of Penrose and Hawking. Accordingly, semiclassical quantum gravity lies outside their scope. Although a number of singularity theorems have been derived under weakened energy conditions, none is directly derived from quantum field theory. Here, we employ a quantum energy inequality satisfied by the quantized minimally coupled linear scalar field to derive a singularity theorem valid in semiclassical gravity. By considering a toy cosmological model, we show that our result predicts timelike geodesic incompleteness on plausible timescales with reasonable conditions at a spacelike Cauchy surface.

28 pages, 5 figures

References in corpus (9)

• Singularity Theorems and Their Consequences
• Fate of gravitational collapse in semiclassical gravity
• Absolute quantum energy inequalities in curved spacetime
• Quantum inequality in spacetimes with small curvature
• An explicit quantum weak energy inequality for Dirac fields in curved spacetimes
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• A Note on the Gannon-Lee Theorem
• Mass Dependence of Quantum Energy Inequality Bounds
• On the global Hadamard parametrix in QFT and the signed squared geodesic distance defined in domains larger than convex normal neighbourhoods

Cited by in corpus (5)

• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Big Bang Singularity Resolution In Quantum Cosmology
• Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes
• Hawking-type singularity theorems for worldvolume energy inequalities
• Quantum Energy Inequalities along stationary worldlines