Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation
J. Fernando Barbero, Madhavan Varadarajan
TL;DR
This paper investigates the complex structure of the constraint hypersurfaces in 2+1 dimensional gravity using the Ashtekar formulation, focusing on a simplified homogeneous model to understand the dynamics.
Contribution
It provides a detailed analysis of the constraint hypersurfaces in the Ashtekar formulation for 2+1 gravity through a simplified homogeneous reduction.
Findings
Constraint hypersurfaces are not manifolds but consist of intersecting sectors.
The paper clarifies how to define consistent dynamics in such a complex structure.
Simplified model offers insights into the structure of 2+1 gravity in Ashtekar variables.
Abstract
The constraint hypersurfaces defining the Witten and Ashtekar formulations for 2+1 gravity are very different. In particular the constraint hypersurface in the Ashtekar case is not a manifold but consists of several sectors that intersect each other in a complicated way. The issue of how to define a consistent dynamics in such a situation is then rather non-trivial. We discuss this point by working out the details in a simplified (finite dimensional) homogeneous reduction of 2+1 gravity in the Ashtekar formulation.
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