Self-dual gravity as a two dimensional theory and conservation laws

Details Self-dual gravity as a two dimensional theory and conservation laws Self-dual gravity as a two dimensional theory and conservation laws

1993-10-03

arxiv.org/abs/gr-qc/9310003v1

Class.Quant.Grav.11:927-938,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, RevTeX, Alberta-Thy-47-93

Scientific paper

10.1088/0264-9381/11/4/011

Starting from the Ashtekar Hamiltonian variables for general relativity, the self-dual Einstein equations (SDE) may be rewritten as evolution equations for three divergence free vector fields given on a three dimensional surface with a fixed volume element. From this general form of the SDE, it is shown how they may be interpreted as the field equations for a two dimensional field theory. It is further shown that these equations imply an infinite number of non-local conserved currents. A specific way of writing the vector fields allows an identification of the full SDE with those of the two dimensional chiral model, with the gauge group being the group of area preserving diffeomorphisms of a two dimensional surface. This gives a natural Hamiltonian formulation of the SDE in terms of that of the chiral model. The conservation laws using the explicit chiral model form of the equations are also given.

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