Structure of the space of solutions of Einstein’s equations: A new variables approach

Abstract

Following Ashtekar’s new Hamiltonian formulation of general relativity [‘‘A new Hamiltonian formulation of general relativity,’’ Syracuse University preprint, 1986; Phys. Rev. Lett. 57, 2244 (1986); Proceedings of the Florence Conference on ‘‘Constrained Systems’’ (World Scientific, Singapore, 1986)], the results of Arms, Fischer, Marsden, and Moncrief [Ann. Inst. H. Poincaré 33, 147 (1980); Ann. Phys. (NY) 144, 81 (1982)] on the structure of the space of solutions of vacuum Einstein equations in the case of space-times admitting a compact Cauchy hypersurface are rederived and extended.