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Lagrangian and Hamiltonian for the Bondi–Sachs metrics

J Korbicz1 and J Tafel2

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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

04.20.Fy Canonical formalism, Lagrangians, and variational principles

MSC

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

Subjects

Gravitation and cosmology

Dates

Issue 13 (7 July 2004)

Received 23 December 2003

Published 14 June 2004



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