Teichmuller Motion of (2+1)-Dimensional Gravity with the Cosmological Constant
Open accessAbstract
The (2+1)-dimensional Einstein gravity with a cosmological constant is studied in the ADM canonical formalism. Adopting York’s time slice, we completely solve the initial-value problem and the time evolution equations with an initla spacelike 2-surface being a closed Riemann surface of genus zero and one. The result in a torus case is that the Teichmüller parameters for the torus follow a geodesic in the Teichmüller space but its motion asymptotically stops due to the presence of the cosmological constant.
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Hamilton's equations from the Poisson brackets reproduce the time dependence (42) of the moduli.
“It may be shown that the version of Hamilton’s equations of motion coming from these brackets reproduces the time dependence (42) of the moduli; see [87, 135] for details.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [135]
The paper gives Hamiltonian time-evolution equations and derives the time dependence of torus moduli, including the Teichmüller parameter in Eq. (5·5). But our copy does not show a derivation from the cited Poisson brackets or compare its result with the citing paper’s Eq. (42). The relevant passages are the Hamilton-equations passage and the Teichmüller-motion discussion; page numbers are unavailable in the indexed copy. (LLM, conf=0.83)
Experimental — accuracy not yet measuredThe semicircular curve is a geodesic in the natural Weil-Petersson (or Poincaré) metric on the torus moduli space.
“Such a curve is a geodesic in the natural Weil-Petersson (or Poincaré) metric on the torus moduli space [159, 135].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [135]
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Research works printed but not linked: 7
- A. Hosoya and K. Nakao, Preprint RRK 89-11 (1989).
- V. Moncrief, Ann. of Phys. 167 (1986), 118.
- J. Soda, Preprint RRK 89-27 (1989).
- C. Misner, K. Thorne and J. Wheeler, Gravitation, Chapter 21 (Freeman, San Francisco, 1973).
- See, for example, J. W. York Jr., J. Math. Phys. 14 (1973), 456.
- H. M. Farkas and 1. Kra, Riemann Surfaces (Springer-Verlag, New York-Heidelberg-Berlin, 1980).
- A. Fisher and A. Tromba, Math. Ann. 267 (1984), 311.
Cited by
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Quantum 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
- Authors
- Fujiwara, Y., & Soda, J.
- Affiliations
- Hiroshima University (JP)
- ORCID
- Soda, J.
- Venue
- Progress of Theoretical Physics
- Publisher
- Oxford University Press (OUP)
- Published
- 1990-04-01
- Volume
- 83
- Issue
- 4
- Pages
- 733-748
- ISSN
- 0033-068X (ISSN-L)
- 1347-4081
- OpenAlex
- W2051202720
- Cited by
- 23
- References
- 0
- Citations by year
- 2020: 2
- FWCI
- 4.05
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Progress of Theoretical Physics (publishedVersion)
- HighWire Press Open Archive (submittedVersion)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Keywords
- three-dimensional gravity, cosmological constant, initial value problems, time evolution equations, Riemann surfaces, torus, Teichmüller space, geodesic motion, asymptotic behavior
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