Mathematical Aspects of Scalar-Tensor Field Theories

scalar-tensor field theory;metric tensor;scalar field;Euler-Lagrange tensor;Brans-Dicke vacuum field equations;static spherically symmetric mass shell;weak field approximation

Horndeski, Gregory Walter

University of Waterloo

关键词: scalar-tensor field theory;    metric tensor;    scalar field;    Euler-Lagrange tensor;    Brans-Dicke vacuum field equations;    static spherically symmetric mass shell;    weak field approximation;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/10928/1/HORNDESKI_GREGORY.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This 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.