Problems in relativity theory and relativistic cosmology

Abstract

The thesis consists of the following three parts: PART I. Chapter I: MOLLER'S THEORY ON ENERGY AND ITS LOCALIZATION AND ITS APPLICATION TO STATIC FIELDS. The difficulties of the Einstein canonical momentum-energy pseudo-tensor are discussed. Moller's new theory on the concept of energy and its localization in general relativity is summarized (and its application by Moller criticized)and applied to find that the energy of the Schwarzschild fields is equal to the gravitational mass of, and resides inside, the material system associated with the fields. Chapter II: THE ELECTROMAGNETIC ENERGY AND THE GRAVITATIONAL MASS OF A CHARGED PARTICLE IN GENERAL RELATIVITY. The electromagnetic energy of the field of a charged particle is calculated using Moller's new theory.The contribution of to the gravitational mass of the particle is investigated. Contrary to currently accepted ideas it is shown that increases the (newtonian) gravitational mass of the particle by an amount which is precisely the mass-equivalence of PART II. ENERGY IN PLANE GRAVITATIONAL WAVES OF FINITE DURATION. The result that the passage of plane gravitational waves impart a relative velocity to test particlesoriginally at relative rest, first obtained by Bondi. Pirani and Robinson using groups of motions, is obtained here by more direct and mathematically easier methods using only the geodesic equations. This effect shows that these waves must carry energy.Moller's result that these waves carry no energy is discussed. PART III. OBSERVABLE RELATIONS IN RELATIVISTIC COSMOLOGY. A new observational criterion likely to solve the " cosmological problem" is formulated. It incorporates the fundamental property that an evolving expanding universe must be more congested at great distances than it is in the cosmic neighbourhood of the observer, while a steady-state universe must exhibit the same congestion at all distances. It is shown that this congestion, measured in suitable statistical terms by the ratio of the angular separation of galaxies from their neighbour galaxies to the angular diameter of the galaxies themselves, is proportional to in an evolving universe; it is independent of Z, the red-shift, ina steady-state universe.The applicability of the criterion and the angular diameter of a galaxy in special relativity are also discussed.