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

R. A. d'Inverno·P. Lambert·J. A. Vickers
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Abstract

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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R. A. d'Inverno, P. Lambert, J. A. Vickers. 2006-04-20. Hamiltonian analysis of the double null 2+2 decomposition of General Relativity expressed in terms of self-dual bivectors. https://doi.org/10.1088/0264-9381%2F23%2F13%2F014

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