Showing papers in "General Relativity and Gravitation in 1970"

Self-interaction and gauge invariance

Abstract: A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g. chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases, they are determined by the conserved currents associated with the initial (linear) gauge invariance of the first kind. Use of first-order formalism leads uniformly to a simple cubic self-interaction.

Spherically symmetric radiation of charge in Einstein-Maxwell theory

Abstract: We give solutions of the Einstein-Maxwell equations describing the emission of charged null fluid from a spherically symmetric body. The electromagnetic field is parallel to the direction of energy propagation, is of orderr −2 at infinity and is not null.

Non-static spherically symmetric clusters of particles in general relativity: I

Abstract: In an ingenious way rotation (but no angular momentum) has been introduced in the case of spherical symmetry by Einstein, who has considered a stationary cluster of particles moving freely under the influence of the gravitational field produced by all of them together. The aim of the present work is to extend his idea to the non-static case, and it seems that under some circumstances instead of an indefinite gravitational collapse there is a minimum of the volume and a bouncing back.

Self-coupled scalar gravitation.

Abstract: The requirement in scalar theories of gravitation that the source of the field includes the trace of its own stress tensor is investigated in two models: (1) The geometrical Nordstr0m theory, which is the conformally flat metric analog of Einstein's theory. (2) The ostensibly non-geometrical flat space system of Freund and Nambu. Both are derived in closed form as cubic self-interacting systems and shown to be equivalent.

Conservation laws in general relativity based upon the existence of preferred collineations

Abstract: The conservation laws based upon the existence of curvature and Ricci collineations are investigated and the results given recently by Katzin, Levine and Davis are reinterpreted and generalized. The concept of a ‘Maxwell collineation’ is introduced and corresponding conservation laws are found.

Universal conventionalism and space-time

Abstract: Geo-chronometric conventionalism (GC) is shown to be part of a more general thesis, universal conventionalism, stating that coordinative definitions are needed in order to compare two measurements of any physical quantity at different space-time points. Two fully elaborated examples of the use of non-standard coordinative definitions in physics are given, demonstrating that the use of these definitions can actually simplify the physical formalism.

Quantum theories of gravity

Abstract: The working out of the implications of the quantum theory and the theory of relativity, and the study of their impact on each other, has been the major preoccupation of theoretical physics in this century. This effort has led to the development of a great number of conceptual schemes having their origins in the formal structure of 'naive' quantmn field theory, primarily within the framework of special relativity. Of much less immediate concern to the physicist at large, but perhaps of equal long range significance, have been a number of efforts in recent years to recast quantum field theory in the setting of general relativity. The latter efforts have involved only a small number of people, but the results achieved are already of some general interest. In narrowest terms the union of general relativity and the quantum theory is called 'the quantization of the gravitational field'. When this nomenclature is used, the almost total irrelevance, to the experimentalist, of the activity in this field becomes obvious. Its significance lies not in the direction of current experimental physics (at least not yet) but in the realm of new perspectives on the foundations of physics and the origins of the universe. It is now clear that no obstacles of principle exist which prevent the unification of the quantum theory and general relativity. Several formalisms providing such unification are very much alive and kicking. These formalisms invoke no new axioms of physics; rather they provide us with new insights into what we already have and what we can yet do with quantum field theory. J. A. Wheeler has attempted to capture the flavor &these unconventional developments in conventional physics by coining, as a replacement for 'quantum theory of gravity', the phrase 'quantum geometrodynamics', which deemphasizes the narrow view of general relativity as a theory of gravity, and suggests a fundamental all-pervading role for the quantized

Gravitation theory as theory of non-Lorentzian transformations of the systems of reference

Abstract: According to the programme of Einstein as discussed with Abraham, gravitation can be described by the bending of the systems of inertia in special relativity. This bending means non-Lorentzian transformations of the systems of reference, depending on the point in space-time. Einstein's equations for the metric imply equations for the transformation matrix, which are also of the same structure.

Embedding of singularities

Abstract: The Friedmann and Kantowski-Sachs models of the universe are embedded in eight-dimensional pseudo-Euclidean spaces in such a way, that their boundaries have the same structure as Geroch'sg-boundary.

Shear in a perturbed Friedmann universe

Abstract: For perturbed Friedmann models of vanishing and positive curvature the time development of shear is computed by means of a linear perturbation theory. As for the smallness of the perturbation functions mathematically exact and physically meaningful conditions are stated. The shear is computed for different stages of the universe.