Showing papers by "Jerzy Lewandowski published in 1992"
TL;DR: In this article, the degeneracy of loop functionals on the Ashtekar phase space of general relativity is studied and the intersection of the set of degenerate points with the real slice of the constraint surface is shown to correspond precisely the Goldberg-Kerr solutions.
Abstract: The small algebra of loop functionals, defined by Rovelli and Smolin, on the Ashtekar phase space of general relativity is studied. Regarded as coordinates on the phase space, the loop functionals become degenerate at certain points. All the degenerate points are found and the corresponding degeneracy is discussed. The intersection of the set of degenerate points with the real slice of the constraint surface is shown to correspond precisely the Goldberg-Kerr solutions. The evolution of the holonomy group of Ashtekar's connection is examined, and the complexification of the holonomy group is shown to be preserved under it. Thus, an observable of the gravitational field is constructed.
29 citations
TL;DR: In this paper, the authors solved the Einstein equations with a cosmological constant for those gravitational fields which have a reduced Ashtekar-spin holonomy group, and proved that the constant is a constant for all such fields.
Abstract: The author solves the Einstein equations with a cosmological constant for those gravitational fields which have a reduced Ashtekar-spin holonomy group.
27 citations