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Lagrangian and Hamiltonian for the Bondi–Sachs metrics

J Korbicz et al 2004 Class. Quantum Grav. 21 3301-3308   doi: 10.1088/0264-9381/21/13/012  Help

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J Korbicz1 and J Tafel2
1 Institute of Theoretical Physics, University of Hannover, Appelstr. 2, D-30167 Hannover, Germany
2 Institute of Theoretical Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
E-mail: jarek@itp.uni-hannover.de and tafel@fuw.edu.pl

Abstract. We calculate the Hilbert action for the Bondi–Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation. For regular null surfaces the Hamiltonian defines an energy which coincides with the Bondi mass and is positive.

PACS number: 04.20.Fy

Print publication: Issue 13 (7 July 2004)
Received 23 December 2003
Published 14 June 2004

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