Mach's principle in general relativity, and other gravitational theories

Abstract

This thesis discusses the extent to which Mach’s principle is incorporated into general relativity. In chapter 1, we consider a vector theory of inertia which attributes the origin of inertial forces to an inductive effect of a moving universe, and which reduces to Newton’s laws of gravitation in a reference frame at rest relative to the “smoothed-out” universe. We then show how general relativity provides a superior presentation of these ideas on the origin of inertia. Chapter 2 is chiefly concerned with boundary conditions on the metric tensor, brought about by a separation of local effects from the general cosmological structure due to the distribution of distant matter. In chapter 3, we consider the compatibility of Mach’s principle with the steady-state theory, and Hoyle’s C-field term is discussed in the light of Mach’s principle. Some solutions of the field equations of general relativity which are incompatible with Mach’s principle are discussed in chapter 4, and in chapter 5 we consider the inertial properties of a test-particle in a homogenous isotropic closed model of the universe. An integral form of Einstein’s equations is presented in chapter 6, involving retarded bi-tensor Green’s functions. A direct-particle interaction theory of gravitation, which reduces to Einstein’s theory in the smooth fluid application is also discussed. [extract from Introduction]