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
3411-3428
Vickers, J.A.
719cd73f-c462-417d-a341-0b042db88634
23 August 2011
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), .
(doi:10.1007/s10714-011-1242-2).
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.
Text
DoubleNull.pdf
- Version of Record
Restricted to Repository staff only
Request a copy
More information
Published date: 23 August 2011
Keywords:
null hamiltonian dynamics, 2+2 formalism, canonical variables
Organisations:
Mathematical Sciences
Identifiers
Local EPrints ID: 204419
URI: http://eprints.soton.ac.uk/id/eprint/204419
ISSN: 0001-7701
PURE UUID: c46b41e7-dfae-4785-9403-90bf6f566b88
Catalogue record
Date deposited: 28 Nov 2011 14:27
Last modified: 15 Mar 2024 02:34
Export record
Altmetrics
Contributors
Author:
J.A. Vickers
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics