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Double null hamiltonian dynamics and the gravitational degrees of freedom

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Abstract

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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Authors and Affiliations

  1. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    J. A. Vickers

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  1. J. A. Vickers
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Correspondence to J. A. Vickers.

Additional information

To Josh Goldberg for providing the inspiration for this work on the Hamiltonian dynamics of GR.

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Vickers, J.A. Double null hamiltonian dynamics and the gravitational degrees of freedom. Gen Relativ Gravit 43, 3411–3428 (2011). https://doi.org/10.1007/s10714-011-1242-2

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