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Cited by 107Black Holes and Theoretical PhysicsQuantum Electrodynamics and Casimir EffectCosmology and Gravitation Theories

Gravitational vacuum polarization. IV. Energy conditions in the Unruh vacuum

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Visser, Matt·1997·Physical Review D
DOI 10.1103/physrevd.56.936
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Abstract

Building on a series of earlier papers, I investigate the various pointwise and averaged energy conditions in the Unruh vacuum. I consider the quantum stress-energy tensor corresponding to a conformally coupled massless scalar field, work in the test-field limit, restrict attention to the Schwarzschild geometry, and invoke a mixture of analytical and numerical techniques. I construct a semianalytic model for the stress-energy tensor that globally reproduces all known numerical results to within $0.8%$, and satisfies all known analytic features of the stress-energy tensor. I show that in the Unruh vacuum (1) all standard pointwise energy conditions are violated throughout the exterior region, all the way from spatial infinity down to the event horizon, and (2) the averaged null energy condition is violated on all outgoing radial null geodesics. In a pair of appendices I indicate a general strategy for constructing semianalytic models for the stress-energy tensor in the Hartle-Hawking and Boulware states, and show that the Page approximation is in a certain sense the minimal Ansatz compatible with general properties of the stress energy in the Hartle-Hawking state.

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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 [44]

    The Discussion (p. 26) describes energy-condition violations in the Unruh vacuum as intrinsically quantum mechanical, supporting the first part of the claim. But it calls the violations ubiquitous, and §2.5 (p. 10) says pointwise violations persist from the horizon to spatial infinity. The paper therefore does not support the claim that the conditions are satisfied at macroscopic scales in the setting it studies. (LLM, conf=0.87)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 2

  1. [1][1] B. S. DeWitt, Phys. Rep. 19 , 295 (1975), see especially pp. 342-345. -
  2. [4][4] 300 Years of Gravitation , edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1987). -

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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
1997-07-15
Volume
56
Issue
2
Pages
936-952
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.56.936
OpenAlex
W2049300938
Cited by
107
References
26
Citations by year
2026: 6 · 2025: 6 · 2024: 4 · 2023: 7 · 2022: 5 · 2021: 7 · 2020: 1 · 2019: 10 · 2018: 6 · 2017: 7 · 2016: 4 · 2015: 7 · 2014: 3 · 2013: 5 · 2012: 3
FWCI
2.31
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)
  • 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 › Atomic and Molecular Physics, and Optics › Quantum Electrodynamics and Casimir Effect
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Keywords
Unruh vacuum, energy conditions, averaged null energy condition, quantum stress-energy tensor, Schwarzschild geometry, event horizon, Hartle-Hawking state, Boulware state

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