Constants of motion for vacuum general relativity

Details Constants of motion for vacuum general relativity Constants of motion for vacuum general relativity

1997-03-30

arxiv.org/abs/gr-qc/9703087v3

Phys.Rev.D56:1831-1835,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, latex, version to appear in Phys. Rev. DR

Scientific paper

10.1103/PhysRevD.56.R1831

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the $SL(2,R)$ principal chiral model with certain `source' terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as explicit functionals on the phase space of Einstein gravity, and are labelled by sl(2,R) indices.

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