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dc.contributor.authorHorndeski, Gregory Walter 19:51:32 (GMT) 19:51:32 (GMT)
dc.description.abstractThis thesis is based on a study of Lagrange scalar densities which are, in general, concomitants of the metric tensor gij (and its first and second derivatives) together with a scalar field ∅ (and its first derivative). Three invariance identities relating the "tensorial derivatives" of this Lagrangian are obtained. These identities are used to write the Euler-Lagrange tensors corresponding to our scalar density in a compact form. Furthermore it is shown that the Euler-Lagrange tensor corresponding to variations of the metric tensor is related to the Euler-Lagrange tensor corresponding to variations of the scalar field in a very elementary manner. The so-called Brans-Dicke scalar-tensor theory of grav­itation is a special case of our previous results and the field equations corresponding to this theory are derived and investigated at length. As a result of studying the effects of conformal transformations on the general Lagrange scalar density it is shown that solutions to the Brans-Dicke field equations are conformally related to solutions to a certain system of Einstein field equations. A detailed study of a particular static, spherically symmetric vacuum solution to the Brans-Dicke field equation is then undertaken and compared with the corresponding Einstein case.en
dc.publisherUniversity of Waterlooen
dc.subjectscalar-tensor field theoryen
dc.subjectmetric tensoren
dc.subjectscalar fielden
dc.subjectEuler-Lagrange tensoren
dc.subjectBrans-Dicke vacuum field equationsen
dc.subjectstatic spherically symmetric mass shellen
dc.subjectweak field approximationen
dc.titleMathematical Aspects of Scalar-Tensor Field Theoriesen
dc.typeMaster Thesisen
dc.pendingfalse Mathematicsen Mathematicsen of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorLovelock, Dr.
uws.contributor.affiliation1Faculty of Mathematicsen

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