Degenerate sectors of the Ashtekar gravity

Degenerate Sectors of the Ashtekar Gravity

This work completes the task of solving locally the Einstein-Ashtekar equations for degenerate data. The two remaining degenerate sectors of the classical 3 + 1 dimensional theory are considered. First, with all densitized triad vectors linearly dependent and second, with only two independent ones. It is shown how to solve the Ashtekar-Einstein equations completely by suitable gauge fixing and ...

Ashtekar Approach to Quantum Gravity

Some of the recent developments in the Ashtekar program of quantization of gravity are discussed in this talk.

Multi-plaquette solutions for discretized Ashtekar gravity

A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll’s discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological manipulations of the lattice loops. Using this topological formulation we find new solutions to the discretized Wheeler-Dewitt equation. These solutions have ...

Horava-Lifshitz theory as a fermionic aether in Ashtekar gravity

Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation

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 wor...