# A semiclassical singularity theorem

@article{Fewster2022ASS, title={A semiclassical singularity theorem}, author={Christopher J. Fewster and Eleni-Alexandra Kontou}, journal={Classical and Quantum Gravity}, year={2022}, volume={39} }

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…

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## References

SHOWING 1-10 OF 76 REFERENCES

The occurrence of singularities in cosmology

- Physics, MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1966

It is shown that singularities of space-time are inevitable if the Einstein equations hold, if matter has normal properties and if the universe satisfies certain reasonable global conditions. The…

Gravitational collapse and spacetime singularities

- Physics
- 2009

The nature of gravitational collapse was the subject of debate and controversy for much of the last century. During the 1960’s and 1970’s our understanding of general relativity consolidated and…

Planck 2018 results. VI. Cosmological parameters

- arXiv preprint arXiv:1807.06209 (2018) .
- 1807

A new derivation of singularity theorems with weakened energy hypotheses

- MathematicsClassical and Quantum Gravity
- 2020

The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions of…

A singularity theorem for Einstein–Klein–Gordon theory

- MathematicsGeneral Relativity and Gravitation
- 2018

Hawking’s singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing…

Integrals of incomplete beta functions, with applications to order statistics, random walks and string enumeration

- MathematicsBrazilian Journal of Probability and Statistics
- 2022

Abstract. We study the probability that one beta-distributed random variable exceeds the maximum of two others, allowing all three to have general parameters. This amounts to studying Euler…

A note on the Gannon–Lee theorem

- Materials ScienceLetters in Mathematical Physics
- 2021

We prove a Gannon–Lee theorem for non-globally hyperbolic Lorentzian metrics of regularity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

Existence and Uniqueness of Solutions of the Semiclassical Einstein Equation in Cosmological Models

- MathematicsAnnales Henri Poincaré
- 2021

We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar…

Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models Ann

- Henri Poincaré
- 2021

Integrals of products of incomplete beta functions with an application to string enumeration

- Mathematics
- 2021

We study Euler transforms of products of two incomplete beta functions, giving closed forms in a variety of special cases, and series expansions of the fully general case. The results are applied to…