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Energy conditions in general relativity and quantum field theory
Open accessAbstract
This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations and discussions. We pay special attention to the role of the equations of motion and to the relation between classical and quantum theories. Pointwise energy conditions were first introduced as physically reasonable restrictions on matter in the context of general relativity. They aim to express e.g. the positivity of mass or the attractiveness of gravity. Perhaps more importantly, they have been used as assumptions in mathematical relativity to prove singularity theorems and the non-existence of wormholes and similar exotic phenomena. However, the delicate balance between conceptual simplicity, general validity and strong results has faced serious challenges, because all pointwise energy conditions are systematically violated by quantum fields and also by some rather simple classical fields. In response to these challenges, weaker statements were introduced, such as quantum energy inequalities and averaged energy conditions. These have a larger range of validity and may still suffice to prove at least some of the earlier results. One of these conditions, the achronal averaged null energy condition, has recently received increased attention. It is expected to be a universal property of the dynamics of all gravitating physical matter, even in the context of semiclassical or quantum gravity.
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“Within standard general relativity the NCC is equivalent to the NEC, and the TCC is equivalent to the SEC.”
From Generic warp drives violate the null energy condition (2022) · cites this paper as [45]
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“An important feature related to the above finite-volume effects is the violation of the Null Energy Condition (NEC - see [18, 19] for reviews), which is known in the case of the Casimir effect, and which has been shown in [12, 13] for tunnelling between degenerate vacua.”
From Double-well instantons in finite volume (2024) · cites this paper as [19]
In the citing paper
“The physicality of warp metrics is established through a set of conditions, known as energy conditions, which are imposed on the stress-energy tensor components [10].”
From Analyzing warp drive spacetimes with warp factory (2024) · cites this paper as [10]
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The Smeared Null Energy Condition
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Metadata
- Authors
- Kontou, E.-A., & Sanders, K.
- Affiliations
- College of the Holy Cross (US)
- Dublin City University (IE)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2020-09-18
- Volume
- 37
- Issue
- 19
- Pages
- 193001
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W3009127927
- Cited by
- 223
- References
- 172
- Citations by year
- 2026: 33 · 2025: 38 · 2024: 56 · 2023: 42 · 2022: 29 · 2021: 22 · 2020: 3
- FWCI
- 10.70
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- UvA-DARE (University of Amsterdam) (submittedVersion)
- Data Archiving and Networked Services (DANS) (submittedVersion)
- arXiv (Cornell University)
- Funders
- H2020 Marie Skłodowska-Curie Actions (744037)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- energy conditions, quantum inequalities, averaged null energy condition, singularity theorems, wormholes, exotic matter, semiclassical gravity, quantum field theory in curved spacetime, equations of motion
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