Large Quantum Gravity Effects: Unforeseen Limitations of the Classical Theory
Open accessAbstract
Three-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axisymmetry. The solution is used to probe several quantum gravity issues. In particular, it is found that if there is an electromagnetic wave of Planckian frequency even with such low amplitude that the curvature of the classical solution is small, the uncertainty in the quantum metric can be very large. More generally, the quantum fluctuations in the geometry are large unless the number and frequency of photons satisfy the inequality $N(\ensuremath{\Elzxh}G\ensuremath{\omega}{)}^{2}\ensuremath{\ll}1$. Results hold also for a sector of the four-dimensional theory (consisting of Einstein-Rosen gravitational waves).
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There is evidence that the matter Hamiltonian is bounded above in (2+1)-dimensional gravity.
“For example, there is evidence that the matter Hamiltonian is bounded above in (2 + 1)-dimensional gravity [27]; perhaps this could cut off radiative contributions to the cosmological constant at an interesting scale.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [27]
In section I (p. 3), the paper says the bounded quantity is the total Hamiltonian of the system, explicitly including gravity. Section I (p. 4) distinguishes that Hamiltonian from H₀, the scalar-field energy, so the cited result does not establish an upper bound on the matter Hamiltonian. (LLM, conf=0.84)
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Experimental — accuracy not yet measuredWork on circularly symmetric midi-superspace models has led to unexpected bounds on the Hamiltonian.
“Certain matter couplings in supergravity have been studied [104, 196], and work on circularly symmetric “midi-superspace models” has led to some surprising results, including unexpected bounds on the Hamiltonian [27, 32, 137, 53, 265, 224].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [27]
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Research works printed but not linked: 3
- [3][3] L. Susskind, J. Math. Phys. 36 , 6397 (1995); G. 't Hooft, Class. Quantum Grav. 11 , 621 (1994); C. Thorne, in Sakharov Conference in Physics, Moscow, Vol. 91, pp 447-54. -
- [7][7] A. Ashtekar and M. Pierri, J. Math. Phys. (in press); gr-qc/9606085. - · arXiv
- [9][9] K. Kuchaˇ r, J. Romano and M. Varadarajan, gr-qc/9608011. - · arXiv
Cited by
Sorted by citations
Quantum geometry of isolated horizons and black hole entropy
Ashtekar, A., Baez, J. C., & Krasnov, K. (2000) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2000.v4.n1.a1 · Cited by 580 · 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
Linear response, validity of semiclassical gravity, and the stability of flat space
Anderson, P. R., Molina-París, C., & Mottola, E. (2003) · Physical Review D · doi:10.1103/physrevd.67.024026 · Cited by 73 · see citing works
Midisuperspace Models of Canonical Quantum Gravity
Torre, C. G. (1999) · International Journal of Theoretical Physics · doi:10.1023/a:1026650212053 · Cited by 42 · see citing works
- Authors
- Ashtekar, A.
- Affiliations
- Pennsylvania State University (US)
- Corresponding author
- Ashtekar, Abhay
- ORCID
- Ashtekar, Abhay
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1996-12-09
- Volume
- 77
- Issue
- 24
- Pages
- 4864-4867
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1978295149
- Cited by
- 89
- References
- 0
- Citations by year
- 2022: 3 · 2021: 4 · 2020: 22 · 2017: 2 · 2015: 2 · 2012: 1
- FWCI
- 4.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Pennsylvania State University
- Division of Mathematical Sciences
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- quantum gravity, three-dimensional gravity, axisymmetric solutions, Maxwell field, Klein-Gordon field, quantum geometry
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