Degenerate Sectors of the Ashtekar Gravity

Details Degenerate Sectors of the Ashtekar Gravity Degenerate Sectors of the Ashtekar Gravity

1999-02-11

arxiv.org/abs/gr-qc/9902037v1

Class.Quant.Grav. 16 (1999) 3057-3069

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, latex

Scientific paper

10.1088/0264-9381/16/10/303

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 Einstein-Ashtekar equations completely by suitable gauge fixing and choice of coordinates. Remarkably, the Hamiltonian weakly Poisson commutes with the conditions defining the sectors. The summary of degenerate solutions is given in the Appendix.

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