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Double null hamiltonian dynamics and the gravitational degrees of freedom

Double null hamiltonian dynamics and the gravitational degrees of freedom
Double null hamiltonian dynamics and the gravitational degrees of freedom
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.
null hamiltonian dynamics, 2+2 formalism, canonical variables
0001-7701
3411-3428
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634

Vickers, J.A. (2011) Double null hamiltonian dynamics and the gravitational degrees of freedom. [in special issue: Physics, Gravity, and the Work of Joshua Goldberg] General Relativity and Gravitation, 43 (12), 3411-3428. (doi:10.1007/s10714-011-1242-2).

Record type: Article

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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Published date: 23 August 2011
Keywords: null hamiltonian dynamics, 2+2 formalism, canonical variables
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 204419
URI: https://eprints.soton.ac.uk/id/eprint/204419
ISSN: 0001-7701
PURE UUID: c46b41e7-dfae-4785-9403-90bf6f566b88
ORCID for J.A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 28 Nov 2011 14:27
Last modified: 19 Jul 2019 01:24

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