Mathematical Aspects of Scalar-Tensor Field Theories
Abstract
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.
Collections
Cite this version of the work
Gregory Walter Horndeski
(2016).
Mathematical Aspects of Scalar-Tensor Field Theories. UWSpace.
http://hdl.handle.net/10012/10928
Other formats
Related items
Showing items related by title, author, creator and subject.
-
Feasibility Study of Ferromagnetic Particulate Path Diversion in Additive Manufacturing
Dombroski, David (University of Waterloo, 2018-04-30)The use of electromagnetic actuator components typically involves a coil comprised of a stack-packed continuous winding, usually layered, and a core material of soft iron or at least a solenoid, similarly constructed, ... -
Ultrasensitive Microwave Near-Field Sensors For Detection, Imaging, and Material Characterization
Albishi, Ali Mohammed (University of Waterloo, 2018-09-25)Affordable, sensitive, selective, fast-responding, label-free sensors are currently in high demand for many of today's applications and technologies, particularly in the food industry, bio-sensing applications, and quality ... -
Assessment of Germanane Field-Effect Transistors for CMOS Technology
Zhao, Yiju; Almutairi, Abdulaziz; Yoon, Youngki (Institute of Electrical and Electronics Engineers, 2017-10-13)Using self-consistent atomistic quantum transport simulations, the device characteristics of n-type and p-type germanane (GeH) field-effect transistors (FETs) are evaluated. While both devices exhibit near-identical off-state ...