The Gauss Map and 2+1 Gravity

Details The Gauss Map and 2+1 Gravity The Gauss Map and 2+1 Gravity

1994-03-04

arxiv.org/abs/gr-qc/9403012v1

Class.Quant.Grav.11:2667-2676,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1088/0264-9381/11/11/009

We prove that the Gauss map of a surface of constant mean curvature embedded in Minkowski space is harmonic. This fact will then be used to study 2+1 gravity for surfaces of genus higher than one. By considering the energy of the Gauss map, a canonical transform between the ADM reduced variables and holonomy variables can be constructed. This allows one to solve (in principle) for the evolution in the ADM variables without having to explicitly solve the constraints first.

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