Degenerate sectors of the Ashtekar gravity

Lewandowski, Jerzy; Wisniewski, J.

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Degenerate sectors of the Ashtekar gravity

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Lewandowski, Jerzy
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Lewandowski, J., & Wisniewski, J. (1999). Degenerate sectors of the Ashtekar gravity. Classical and Quantum Gravity, 16(10), 3057-3069.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-58D1-3

Abstract

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 choice of coordinates. Remarkably, the Hamiltonian weakly Poisson commutes with the conditions defining the sectors. The summary of degenerate solutions is given in an appendix.