Mathematical Aspects of Scalar-Tensor Field Theories
MetadataShow full item record
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.
Cite this work
Gregory Walter Horndeski (2016). Mathematical Aspects of Scalar-Tensor Field Theories. UWSpace. http://hdl.handle.net/10012/10928
Showing items related by title, author, creator and subject.
Ang, Jason (University of Waterloo, 2003)For producing realistic images, reflection is an important visual effect. Reflections of the environment are important not only for highly reflective objects, such as mirrors, but also for more common objects such as ...
Shafiee, Mohammad Javad (University of Waterloo, 2017-02-21)Structural data modeling is an important field of research. Structural data are the combination of latent variables being related to each other. The incorporation of these relations in modeling and taking advantage of those ...
Wapler, Matthias Christian (University of Waterloo, 2009-09-03)Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". ...