(2+1)-dimensional pure gravity for an arbitrary closed initial surface
Open accessAbstract
The (2+1)-dimensional pure Einstein gravity is studied in the ADM formalism. The authors solve the initial value and the time evolution problems with a closed Riemann surface being an initial surface, choosing the time slicing so that the trace of the extrinsic curvature is independent of spatial coordinates. The possible topology of the 2-surface is either a torus or a Riemann surface of genus g>or=2. It is shown that the moduli parameters of the torus follow the geodesic curve in the moduli space.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The metric formalism can be used to give a full description of the solutions of the vacuum field equations, at least for spacetimes with topology R×Σ.
“As Moncrief [206] and Hosoya and Nakao [159] have shown, this metric formalism can also be used to give a full description of the solutions of the vacuum field equations, at least for spacetimes with the topology ℝ × Σ.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [159]
The Introduction describes an ADM metric approach for vacuum spacetimes with topology Σ × ℝ, and the Summary says the authors have completely solved the classical equations. But the Summary also says they could not explicitly demonstrate the motion of the moduli in the general case, so the claim of a full description for all such spacetimes overstates what the paper establishes. (LLM, conf=0.82)
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 [159]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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
Flagged first, then by citations
Research works printed but not linked: 4
- The topological Chern-Simons formulation is first given by Horowitz G T 1988 preprint NSF-ITP-88-178
- Arnowitt R, Deser S and Misner C W 1962 GraDitation ed L Witten (New York: Wiley)
- Farkas H M and Kra I 1980 Riemann Surfaces (Berlin: Springer)
- Achucarro A and Townsend P 1986 Phys. Lett. 180B 85 to a Hamiltonian system over Teichmuller space Yale preprint
Cited by
Sorted by citations
Black hole in three-dimensional spacetime
Bañados, M., Teitelboim, C., & Zanelli, J. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.1849 · Cited by 3,831 · see citing works
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
- Hosoya, A., & Nakao, K.
- Affiliations
- Hiroshima University (JP)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1990-02-01
- Volume
- 7
- Issue
- 2
- Pages
- 163-176
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2037306905
- Cited by
- 81
- References
- 1
- Citations by year
- 2026: 1 · 2024: 1 · 2023: 2 · 2020: 5 · 2018: 1
- FWCI
- 5.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Institutional Repositories DataBase (IRDB) (submittedVersion)
- Tokyo Tech Research Repository (Tokyo Institute of Technology) (submittedVersion)
- Funders
- Aspen Center for Physics
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- three-dimensional gravity, compact Riemann surfaces, initial value problems, time evolution, ADM formalism, extrinsic curvature, torus topology, moduli spaces, geodesic curves, higher genus surfaces
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
