Entropy versus action in the (2 + 1)-dimensional Hartle-Hawking wave function
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In most attempts to compute the Hartle-Hawking "wave function of the Universe" in Euclidean quantum gravity, two important approximations are made: the path integral is evaluated in a saddle-point approximation, and only the leading (least action) extremum is taken into account. In (2 + 1)-dimensional gravity with a negative cosmological constant, the second assumption is shown to lead to incorrect results: although the leading extremum gives the most important single contribution to the path integral, topologically inequivalent instantons with larger actions occur in great enough numbers to predominate. One can thus say that in 2 + 1 dimensions, and possibly in 3 + 1 dimensions as well, entropy dominates the action in the gravitational path integral.
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For Λ < 0, the Hartle-Hawking wave function acquires infinite peaks at certain specific spatial geometries because topologically complicated manifolds dominate the path integral.
“In this case, the Hartle-Hawking wave function has been examined as well, and it has been shown that the wave function acquires infinite peaks at certain specific spatial geometries: Again, topologically complicated manifolds whose individual contributions are small occur in large enough numbers to dominate the path integral, and “entropy” wins out over “action” [69].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [69]
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Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
Loss of incoherence and determination of coupling constants in quantum gravity
Giddings, S. B., & Strominger, A. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90109-5 · Cited by 562 · see citing works
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Research works printed but not linked: 9
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The (2 + 1)-dimensional black hole
Carlip, S. (1995) · Classical and Quantum Gravity · doi:10.1088/0264-9381/12/12/005 · Cited by 609 · see citing works
Self-citationQuantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
Self-citationCarlip, S. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acceb4 · Cited by 41 · see citing works
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- Authors
- Carlip, S.
- Affiliations
- University of California, Davis (US)
- Corresponding author
- Carlip, S.
- ORCID
- Carlip, S.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1992-11-15
- Volume
- 46
- Issue
- 10
- Pages
- 4387-4395
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2125244127
- Cited by
- 24
- References
- 2
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 2 · 2022: 1
- FWCI
- 1.56
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- 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)
- Funders
- U.S. Department of Energy (FG0391ER40674)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Hartle-Hawking wave function, Euclidean quantum gravity, three-dimensional gravity, negative cosmological constant, instantons, saddlepoint approximation, gravitational path integral, quantum cosmology
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