Causal structure and diffeomorphismsm in Ashtekar's gravity

Abstract

A manifestly diffeomorphism invariant extension of Einstein gravity is constructed, which includes singular metrics, and whose ADM formulation is Ashtekar's gravity. The latter is shown to be locally equivalent to the covariant theory. It turns out that exactly those kinds of degenerate four dimensional metrics are allowed which do not destroy the causal structure of spacetime. It is also shown that Ashtekar's gravity possesses an extension that provides a local SO(3,C) invariance, without complexifying or changing the signature of the metric.