Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors

Details Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors

2006-04-20

arxiv.org/abs/gr-qc/0604084v1

Class.Quant.Grav. 23 (2006) 4511-4522

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX, uses iopart.cls, submitted to Class. Quantum Grav

Scientific paper

10.1088/0264-9381/23/13/014

In this paper we obtain a 2+2 double null Hamiltonian description of General Relativity using only the (complex) SO(3) connection and the components of the complex densitised self-dual bivectors. We carry out the general canonical analysis of this system and obtain the first class constraint algebra entirely in terms of the self-dual variables. The first class algebra forms a Lie algebra and all the first class constraints have a simple geometrical interpretation.

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