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Cited by 148Black Holes and Theoretical PhysicsRelativity and Gravitational TheoryCosmology and Gravitation Theories

Gravitational vacuum polarization. II. Energy conditions in the Boulware vacuum

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Visser, Matt·1996·Physical Review D
DOI 10.1103/physrevd.54.5116
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Abstract

Building on techniques developed in the preceding paper, I investigate the various pointwise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally coupled massless scalar field in the Boulware vacuum. I work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. In contradistinction to the case of the Hartle-Hawking vacuum, wherein violations of the energy conditions were confined to the region between the event horizon and the unstable photon orbit, I show that in the Boulware vacuum (1) all standard (pointwise and averaged) energy conditions are violated throughout the exterior region, all the way from spatial infinity down to the event horizon, and (2) outside the event horizon the standard pointwise energy conditions are violated in a maximal manner: They are violated at all points and for all null or timelike vectors. (The region inside the event horizon is considerably messier and of dubious physical relevance. Nevertheless, the standard pointwise energy conditions seem to be violated even inside the event horizon.) I argue that this is highly suggestive evidence, pointing to the fact that general self-consistent solutions of semiclassical quantum gravity might not satisfy the energy conditions and may in fact for certain quantum fields and certain quantum states violate all the energy conditions.

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  • There are signs that the weak and null energy conditions may be violated at the quantum-microscopic scale, although they seem to be satisfied at macroscopic scales.

    “Itis worth mentioning that there are signs that WEC and NECmaybeviolated at the quantum-microscopic scale [4049], although they seem to be satisfied at the macroscopic scales.”

    From Alcubierre warp drive in spherical coordinates with some matter configurations (2023) · cites this paper as [42]

    The paper supports the possibility of quantum violations of the WEC and NEC, but contradicts the claim that these conditions seem satisfied at macroscopic scales. The Introduction (p. 2) reports violations throughout the exterior region, and the Discussion (p. 7) says violations would persist outside a star or planet, though they would be tiny. (LLM, conf=0.86)

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Authors
Visser, M.
Affiliations
Washington University in St. Louis (US)
Corresponding author
Visser, Matt
ORCID
Visser, Matt
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1996-10-15
Volume
54
Issue
8
Pages
5116-5122
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.54.5116
OpenAlex
W2156017642
Cited by
148
References
21
Citations by year
2026: 4 · 2025: 8 · 2024: 7 · 2023: 8 · 2022: 7 · 2021: 10 · 2020: 7 · 2019: 15 · 2018: 2 · 2017: 13 · 2016: 8 · 2015: 11 · 2014: 7 · 2013: 4 · 2012: 5
FWCI
2.77
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Keywords
Boulware vacuum, energy conditions, quantum stress-energy tensor, conformally coupled scalar field, Schwarzschild geometry, event horizon, semiclassical gravity

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