Scalar-tensor theories of gravitation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics

Abstract

The problem the writer wishes to consider here is essentially one related to the classical field description of Nature. The framework of General Relativity provides a theory for the geometry of the four dimensional space-time manifold and at the same time gives a description of the gravitational field in terms of the metric tensor, while the electromagnetic field can be interpreted in terms of a particular second rank, skew-symmetric tensor — the covariant curl of a vector field defined on the manifold. However the scalar field, the simplest geometric object that could be defined on the manifold, does not seem to be experimentally evident when it is interpreted as a third, classical long range field. In spite of this lack of experimental evidence and as there appears to be no theoretical objection to the existence of such a long range field, the problem is to introduce the scalar field into the classical scheme of things and to construct a viable theory containing all three long range fields. [From Introduction]