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Cited by 106Black Holes and Theoretical PhysicsCosmology and Gravitation TheoriesRelativity and Gravitational Theory

Gravitational vacuum polarization. I. Energy conditions in the Hartle-Hawking vacuum

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Visser, Matt·1996·Physical Review D
DOI 10.1103/physrevd.54.5103
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Abstract

When a quantum field theory is constructed on a curved background spacetime, the gravitationally induced vacuum polarization typically induces a nonzero vacuum expectation value for the quantum stress-energy tensor. It is well known that this gravitational vacuum polarization often violates the pointwise energy conditions and sometimes violates the averaged energy conditions. In this paper I begin a systematic attack on the question of where and by how much the various energy conditions are violated. To keep the discussion manageable, I work in the test-field limit, and focus on conformally coupled massless scalar fields in Schwarzschild spacetime, using the Hartle-Hawking vacuum. The discussion invokes a mixture of analytical and numerical techniques, and critically compares the qualitative behavior to be expected from the Page approximation with that adduced from the numerical calculations of Anderson, Hiscock, and Samuel. I show that the various pointwise energy conditions are violated in a series of onionlike layers located between the unstable photon orbit and the event horizon, the sequence of violations being DEC, WEC, and (NEC+SEC). Furthermore, the ANEC is violated for some of the null geodesics trapped in this region. Having established the basic machinery in this paper, the Boulware vacuum will be treated in a companion paper, while studies of the Unruh vacuum should be straightforward, as should extensions to nonconformal couplings, massive scalars, and Reissner-Nordstr\"om geometries.

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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 [41]

    The opening summary (p. 1) reports WEC and NEC violations caused by quantum vacuum polarization. The Discussion (p. 17) says energy conditions are satisfied outside the unstable photon orbit, but this is a result for a particular field and black-hole spacetime, not a general finding that the conditions hold at macroscopic scales or fail specifically at microscopic scales. (LLM, conf=0.86)

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Cites

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Research works printed but not linked: 3

  1. [4]S. W. Hawking and W. Israel, editors. 300 Years of Gravitation . Cambridge University Press, Cambridge, England, 1987.
  2. [7]´ E. ´ E. Flanagan and R. M. Wald. Does backreaction enforce the averged null energy condition in semiclassical gravity? gr-qc/9602052 , 1996. · arXiv
  3. [40]L. H. Ford and T. A. Roman. Averaged energy conditions constrain traversable wormhole geometries. gr-qc/9510071 , 1995. · arXiv

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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
5103-5115
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.54.5103
OpenAlex
W2049397965
Cited by
106
References
40
Citations by year
2026: 5 · 2025: 7 · 2024: 2 · 2023: 6 · 2022: 4 · 2021: 5 · 2020: 1 · 2019: 6 · 2018: 2 · 2017: 5 · 2016: 4 · 2015: 9 · 2014: 6 · 2013: 6 · 2012: 3
FWCI
3.00
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 › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
energy conditions, Hartle-Hawking vacuum, conformally coupled scalar field, Schwarzschild metric, averaged null energy condition, weak energy condition, dominant energy condition, null energy condition, photon orbits, event horizon, quantum stress-energy tensor

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