The phase space of (2 + 1)-dimensional gravity in the Ashtekar formulation

Abstract

The Ashtekar formulation of 2+1 gravity differs from the geometrodynamical and Witten descriptions when the two-metric is degenerate. We study the phase space of 2+1 gravity in the Ashtekar formulation to understand these degenerate solutions to the field equations. In the process we find two new systems of first-class constraints which describe part of the degenerate sectors of the Ashtekar formulation. One of them also generalizes the Witten constraints. Finally we argue that the Ashtekar formulation has an arbitrarily large number of degrees of freedom in contrast to the usual descriptions.