Double null hamiltonian dynamics and the gravitational degrees of freedom

Details Double null hamiltonian dynamics and the gravitational degrees of freedom Double null hamiltonian dynamics and the gravitational degrees of freedom

Dec 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011gregr..43.3411v&link_type=abstract

General Relativity and Gravitation, Volume 43, Issue 12, pp.3411-3428

Physics

Null Hamiltonian Dynamics, 2+2 Formalism, Canonical Variables

Scientific paper

In this paper we review the Hamiltonian description of General Relativity using a double null foliation. We start by looking at the 2+2 version of geometrodynamics and show the role of the conformal 2-structure of the 2-metric in encoding (through the shear) the 2 gravitational degrees of freedom. In the second part of the paper we consider instead a canonical analysis of a double null 2+2 Hamiltonian description of General Relativity in terms of self-dual 2-forms and the associated SO(3) connection variables. The algebra of first class constraints is obtained and forms a Lie algebra that consists of two constraints that generate diffeomorphisms in the two surface, a constraint that generates diffeomorphisms along the null generators and a constraint that generates self-dual spin and boost transformations.

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