Gravitational radiation from nearly Newtonian systems
Gravitational radiation from nearly Newtonian systems
A method of examining gravitational radiation from nearly Newtonian systems is presented. Using the Cartan formulation of Newtonian gravity, a one parameter family of space-times which have a strict Newtonian limit is constructed. An expression for the initial null data in terms of the Newtonian potential is obtained in the Newtonian limit. Using this, the problem is formulated as a series in the Newtonian parameter. The series expansions for the sources of the Bianchi identities are obtained to third order in both the vacuum and non-vacuum cases. A simple technique is presented for determining whether a particular source term gives rise to asymptotically flat null data. The far field quadrupole formula is derived in a leading approximation and a method for obtaining error bounds is discussed. Additionally, a method for solving Einstein's equations is shown. This involves expressing the Ricci identities as a matrix Riccati equation and a system of linear matrix equations. A comparison of the formalisms of Bondi and Newman Penrose is presented and explicit correspondences between the hypersurface constraint equations and the Ricci identities are shown.
University of Southampton
1989
Kirk, Ewan McKinnon
(1989)
Gravitational radiation from nearly Newtonian systems.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
A method of examining gravitational radiation from nearly Newtonian systems is presented. Using the Cartan formulation of Newtonian gravity, a one parameter family of space-times which have a strict Newtonian limit is constructed. An expression for the initial null data in terms of the Newtonian potential is obtained in the Newtonian limit. Using this, the problem is formulated as a series in the Newtonian parameter. The series expansions for the sources of the Bianchi identities are obtained to third order in both the vacuum and non-vacuum cases. A simple technique is presented for determining whether a particular source term gives rise to asymptotically flat null data. The far field quadrupole formula is derived in a leading approximation and a method for obtaining error bounds is discussed. Additionally, a method for solving Einstein's equations is shown. This involves expressing the Ricci identities as a matrix Riccati equation and a system of linear matrix equations. A comparison of the formalisms of Bondi and Newman Penrose is presented and explicit correspondences between the hypersurface constraint equations and the Ricci identities are shown.
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Published date: 1989
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Local EPrints ID: 461605
URI: http://eprints.soton.ac.uk/id/eprint/461605
PURE UUID: 810c8965-4d6b-46c3-a825-220d47017463
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Date deposited: 04 Jul 2022 18:50
Last modified: 04 Jul 2022 18:50
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Author:
Ewan McKinnon Kirk
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