Evolution of Degenerate Space-Time from Non-Degenerate Initial Value in Ashtekar's Formalism

The possibility of evolving a degenerate space-time from non-degenerate initial value in Ashtekar's formalism is considered in a constructed example. It is found that this possibility could be realized in the time evolution given by Ashtekar's equations, but the topology change of space makes it fail to be a Cauchy evolution.     

Double Complex (Anti-)self-dual Variables and a Related Double Action in Four-dimensional Gravity

In this paper double dual transformations anddouble complex (anti-)self-dual variables infour-dimensional gravity are given by using the doublecomplex function method. A double action with doublecomplex anti-self-dual variables is proposed, hence thedouble complex (anti-) self-dual gravitational theory isestablish. Finally, the analytic continuation from thedouble action to the Euclidean action is discussed, and some given results are here extended intoa double form.     

Do Bosons Feel Spin Frames?

In order to allow a coherent dynamicalspinor-matter coupling in a previous paper of ours weintroduced new variables to describe gravitationalfield, related to spin structures and called spinframes. A natural action of spacetime diffeomorphismson spin frames cannot be defined. Accordingly they mustbe treated as a sort of gauge fields, i.e. they must beconsidered to be covariant with respect to automorphisms of some suitable principal bundle. In thispaper we analyze what happens when general bosonicmatter and gauge fields interacting with gravity(described by spin frames) are considered. As should beexpected, such a theory reduces to a theory in whichgravity is described by means of a metric alone.Conserved quantities are also considered indetail.