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(2+1)-dimensional pure gravity for an arbitrary closed initial surface

A Hosoya and K Nakao

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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.


PACS

04.60.-m Quantum gravity

02.40.-k Geometry, differential geometry, and topology

04.20.Ex Initial value problem, existence and uniqueness of solutions

MSC

30Fxx Riemann surfaces

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 2 (February 1990)



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