CONSTANTS OF MOTION FOR VACUUM GENERAL-RELATIVITY

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commut ing spacelike Killing vector fields, may be written as the equations o f the SL(2,R) principal chiral model with certain ''source'' terms. Us ing this formulation, we give a procedure for generating an infinite n umber of nonlocal constants of motion for this sector of the Einstein equations. The constants of motion arise as explicit functionals on th e phase space of Einstein gravity, and are labeled by s1(2,R) indices.